Magnetic Effet of Electric Current

Magnetic Effet of ElectricCurrent

15

COMPREHENSIVE REVIEW

1. Basic Concept

i) The magnetic effect of electric current was

discovered by Oersted in 1820. It was

mathematically explained by Biot and

Savart.

ii) The product of current I and elementary

length d of the current carrying conductor

is called current element. Thus, current

element is given by Id . The direction of

current element is same as that of electric

current.

2. Magnetic field, Magnetic induction

The region or space around a magnet, current

carrying conductor or a moving charge, in which

magnetic effect can be experienced is called

magnetic field.

i) The magnetic field strength is called

magnetic induction. It is denoted by B.

ii) Magnetic induction is a vector quantity.

iii) The magnetic induction may be geometri-

cally represented by the lines of magnetic

induction in the same way as the electric

field is represented by the electric field lines.

iv) The lines of magnetic induction are closed

curves (continuous curves). However, it may

be remembered that the electric field lines

are discontinuous curves originating from the

+VE charge and ending at the –VE charge.

v) The lines of magnetic induction for uniform

magnetic field are parallel and equally

spaced. But that for the non-uniform

magnetic field are curves or unequally spaced

or both.

vi) The SI unit of magnetic induction is tesla

(T) or weber/metre2 (Wb/m2).

vii) The cgs unit of magnetic induction is

maxwell/centimetre2 (Mx/cm2) or gauss

(Gs).

viii) 1 T = 104 Gs

MAGNETIC EFFECT OF ELECTRIC CURRENT ( 146 )

3. Biot Savart Law

The magnetic field due to a current element

is given by the following relation.

0

2

ˆId rB

4 r

It is called Biot Savart law. See the figure

below :

Fig. 3.1

Here I d the current element and P is the

observation point where magnetic field due to the

current element is dB.

Also, here r

is the position

vector of the observation point from the current

element.

In the above expression 0 is a magnetic

constant for free space. It is called permeability

of free space.

i) If be the angle between Id and r

, then :

0

2

IdB sin

4 r

ii) The unit of magnetic field B is called tesla

(T).

iii) 0 = 4 10–7 T mA–1.

iv) B

is perpendicular to both Id and r.

v) The current element plays the same role in

producing a magnetic field as the point

charge does in producing electric field.

vi) Biot Savart law is the analogue of the

coulomb's law in electrostatics.

4. The Magnetic field due to a straight current

carrying conductor

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Consider a straight conductor carrying a

current I. (See the figure below) :

Fig. 4.1

The magnetic field due to it at a point P is

given by:

01 2

IB (sin sin )

4 r

Here, 2 1PL r, E PL &

1 2E PL

i) If the conductor be infinitely long, then

1=

2= 900. Hence magnetic field due to

infinite straight current carrying conductor

is given by the following relation.

0 IB

4 r

(sin 900 + sin 900)

or 0 2IB

4 r

ii) The direction of the magnetic field is given

by the Right Hand Fist Rule as follows :

Fig. 4.2

Imagine to catch the current carrying

straight conductor in the right hand fist such

that the out stretched thumb gives the

direction of the current. Then, the fingers

give the direction of the magnetic field lines.

iii) Magnetic field lines due to a straight current

carrying conductors are concentric circles

with their centres on the conductor.

iv) Magnetic field at the end of an infinite

current carrying conductor is given by the

following relation :

0 end

IB

4 r

Note that, end

1B B

2

v) Magnetic field at the end of a straight

conductor of finite length is given by :

0 IB sin

4 r

See figure below for other details.

Fig. 4.3

5. Magnetic field on the axis of a current

carrying circular coil

Figure shows a circular coil of radius R.

XOX' is its axis. P is a point on its axis and OP = r.

The current through the coil is I. The magnetic

field due to the current carrying coil at P is given

by the following relation :

2

0

2 2 3/ 2

2 R IB N

4 (R r )

Fig. 5.1

where N is the number of turns of the coil.

i) The magnetic field at the centre of the coil

is given by :

0c

2 IB N

4 R

In this case r = 0.

ii) The direction of the magnetic field is given

by the right hand fist rule as follows :

Fig. 5.2





Catch the axis of the coil in the right hand

fist such that the fmgers curl in the direction

of the current. Then the outstretched thumb

gives the direction of the magnetic field.

iii) The current carrying coil behaves as a

magnetic dipole of moment :

2

mP N R I N (area of coil) I

iv) The unit of magnetic dipole moment Pm is

Am2.

v) At a far away point, where r >> R, we find :

2

0 0 m

3 3

2p2 R IB N

4 r 4 r

vi) The polarity of the current carrying

magnetic dipole can be determined as

follows. Look at the face of the coil. If the

current through the coil is counter clockwise,

then that face is north pole. And if the current

is clockwise, then that face is south pole.

See the figure given above :

Fig. 5.3

vii) Magnetic field due to a current carrying arc

subtending angle at the centre is given by :

0

arc

2 IB

4 R 2

Fig. 5.4

viii) The magnetic field due to a current carrying

circular coil on its axis varies with distance

as follows :

Fig. 5.5

Here O is the centre of the coil and

XOX' is the axis of the coil.

ix) Some special current configurations

a)

Fig. 5.6

0 0c

2 I IB

4 R 2 4 R

Here, the straight wire behaves as if it

is infinite conductor passing through C,

hence it produces no magnetic field at C.

b)

Fig. 5.7

0 0 0c

2 I 2I 2IB ( 1)

4 R 4 R 4 R

c)

Fig. 5.8

0 0 0c

2 I 2I 2IB ( 1)

4 R 4 R 4 R

d)

Fig. 5.9

0 0

c

2 I 2IB

4 R 2 4 R

0 2I

14 R 2

e)

Fig. 5.10





0 0c

2 I 2I 1B

4 R 2 4 R 2

0 2I 1

4 R 2 2

f)

Fig. 5.11

0

c

2 I 2B

4 R 2

g)

Fig. 5.12

0 0c

2 1

2 I 2 2 I 2B

4 R 2 4 R 2

0

2 1

2 1 12 I

4 2 R R

h)

Fig. 5.13

Bc = 0 due to circular portion because

= 900.

Fig. 5.14

Here 1 2I (2 ) I

Because the resistances of the two parts

are proportional to (2 – ) & respectively.

Also :

0 01 2c

2 I 2 I2B

4 R 2 4 R 2

Hence, Bc = 0 due to circular portion = 900.

j)

Fig. 5.15

cB 0

k)

Fig. 5.16

cB 0

l)

Fig. 5.17

cB 0

m)

Fig. 5.18

0 00c

IB sin 45 sin 45 [4]

4 ( / 2)

0 02I 1 8I

2 4 [ 2]4 4 I2





6. Ampere's circuital law

i) The line integral of the magnetic field around

a closed path is 0 times the total current

enclosed by therath. That is :

0B d I

ii) Magnetic field in the space enclosed by the

circular toroid (or toroidal solenoid) is given

by :

0B nI

Fig. 6.1

where n = number of turns per unit length

of the toroidal solenoid and I is the current

through it.

a) The magnetic field in the space outside that

enclosed by the toroidal solenoid is zero.

b) Magnetic field due to a toroidal solenoid is

independent of its radius.

7. Magnetic field due to a straight solenoid

Well within it and on the axis is given by :

0B nI

where n = number of turns per unit length

and I is the current in the coil.

Fig. 7.1

i) The straight solenoid can be treated as a

toroid of infinite radius. Remember, that the

magnetic field due to a toroid is independent

of its radius.

ii) The current carrying solenoid behaves like

a bar magnet. Its polarity can be determined

by using the right hand fist rule in the same

way as we do for the current carrying coil.

iii) Magnetic field at the end of a long current

carrying solenoid is nearly :

end 0

1B nI

2

iv) Magnetic field at a point on the axis of the

solenoid in general is given by the following

relation :

Fig. 7.2

01 2

nIB [cos cos ]

2

v) Magnetic force between two parallel and

infinite current carrying conductors is given

by the following relation :

Fig. 7.3

0 1 2m /

2I IF

4 r

Here Fm/

is the force per unit length of the

either wire. Here r is the separation between the

wires.

vi) The force is attractive when the currents

are in the same direction.

vii) The force is repulsive when the currents are

in opposite direction.

viii) Magnetic force between the two charges

q1 and q

2 moving with velocities

1 and

2

parallel to each other is given by the following

relation :

0 1 1 1 2m

q qF

4 r

Fig. 7.4

Here, r is the separation between the

charges.





ix) If the charges are similar and moving in the

same direction, then the magnetic force

between the charges is attractive.

The magnetic force is repulsive if the

charges move in opposite directions.

Fig. 7.5

x) If the charges are dissimilar and moving in

the same direction, then the magnetic force

is repulsive.

The magnetic force is attractive if the

dissimilar charges move in the opposite

direction.

Note that, the electrostatic force continues

to be repulsive between similar charges and

attractive between dissimilar charges.

Also e mF F

xi) The ratio of the electric force Fe and the

magnetic force Fm between two moving

charges is as follows :

2

0 1 2e

2

m 0 1 2 1 2

1/ 4 q q / rF

F ( / 4 )(q q / r )

0 0 1 2

1

or

2

e

m 1 2

F c

F

where, c = 0 0

1

= speed of light.

8. A test charge q0 fired with a velocity

in a

magnetic field B

Figure below shows a magnetic field B

. AA

test charge q0 enters it with a velocity

making

angle with B

.

Fig. 8.1

i) The magnetic force on the test charge is

given by :

m 0F q B

orm 0F q Bsin

ii) The magnetic force depends on q0, , B as

well as the angle between

and B

.

iii) mF

is perpendicular to both

as well as

B

.

iv) Since mF

is perpendicular to

, therefore

the magnetic force mF

acts as a centripetal

force.

v) Since mF ,

therefore the power dissipated

mF 0.

That is why, no energy is dissipated by

the magnetic field on the test charge.

Consequently, the speed of the particle

remains constant.

vi) The test charge describes a helical path with

axis parallel to B

if 00 or 1800 or 900.

vii) When = 00 or 1800,

we find Fm = q

0 B sin = 0, hence

the particle moves along a straight line path.

That is, the particle goes undeviated.

viii) If = 900, the particle describes a circular

path in a plane perpendicular to B

.

ix) If r be the radius of the helical path, then

2

m 0

mF q Bsin

r

where m is the mass of the test charge.

That is : 0

mr

q Bsin





And if B,

that is = 900, then :

0

mr

q B

x) The time period (T), the frequency of

revolution (f) and the angular frequency ()

are given by the following relation.

2

0

1 2 2 r 2 mT

f sin q Bsin

For B,

we find = 900, hence

0

1 2 2 mT

f q B

xi) The pitch of the helical path is given by,

p ( cos ) T

2

0

2 mcos

q Bsin

2

0

2 m cos

q B sin

For B,

we find = 900, we find p = 0.

In such a case the particle describes a

circular path in a plane perpendicular to B

.

xii) The centripetal acceleration of the test

charge is given by :

2

0mc

q BsinFa

r m m

For = 900, we have 0c

q Ba

m

xiii) The momentum of the charged particle at

any instant is :

p m

Its direction changes, but magnitude remains

unchanged.

xiv) Following characteristics connected with a

test charge fired through a magnetic field

do not depend on the velocity with which

the particle enters the magnetic field :

a) Time period

b) Frequency

c) Angular frequency

xv) Questions may be asked to compare the

motion of following particles in a magnetic

field.

0

0

q / mMass (m)Charge

Particle Symbol compared to comparedq

proton to proton1

Electron e e 18401840

1Positron e e 1840

1840Proton p 1 e 1

1Deutron d 2 e

21

-particle 4 2e2

xvi) For the particle fired perpendicular to the

magnetic field, we find :

a)0 0

m mr r

q B q

b)0 0

2 m mT T

q B q

c) 0q1f f

T m

d) 0q2

T m

e) 0 0c c

q B qa a

m m

Same is true for Fm :

xvii) Comparative values of r, T, f, , ac, F

m for e,

p, d and -particles entering the magnetic

field with the same velocities.

a) d pr r 2r and p

e

rr

1840

b) d pT T 2T and p

e

TT

1840

c)p

d

ff f

2 and e pf 1840 f

Same is true for and ac as well as F

m.

xviii) When the particles enter the magnetic field

with the same momenta, then :

0

mr

q B





That is 0

1r ,

q because

m

B

is constant.

Hence, ae p d

rr r r

2

9. Cyclotron

The cyclotron consists of two dees, placed in a

strong magnetic field. Oscillating electric field is

applied to the two dees from an oscillator. The

magnetic field is perpendicular to the electric field.

The electric field exists only across the gap

between the dees.

i) The charged particles are accelerated while

crossing the gap and move along circular

paths of radius.

0

mr

q B

This happens in accordance with the

description of motion of the charged particle

in the previous section.

ii) As the charged particle is accelerated while

crossing the gap its kinetic energy increases

and the radius of the circular path also

increases.

But the frequency of revolution remains

unchanged so long as mass remains constant.

iii) Cyclotron cannot be used to accelerate the

electrons because, the electrons move with

velocities very near the velocity of light.

Hence appreciable increase in mass occurs

according to the relation :

0

2 2

mm

1 / c

Hence, the frequency of revolution also

changes.

10. Motion of charged particle in electric field

i) When a charged particle is fired in an electric

field E,

the force acting on the test charge

q0 is given by :

e 0F q E

ii) eF

is either parallel to E

when q0 is +VE

or opposite to E

when q0 is –VE.

iii) Suppose the instantaneous velocity of the

particle is

. Then it is found that Fe is

independent of .

iv) The particle goes undeviated through E

if

the angle between

and E

is 00 or 1800.

v) The charged particle describes a parabolic

path in E

when the angle between

and

E

is other than 00 or 1800.

vi) The particle gains or loses energy as follows :

00 0

0 0

0 0

0 0

0 0

Angle betweenNature of Gain or losscharge (q ) of energy and E ( )

+VE 90 90 Gain

+VE 90 270 Loss

VE 90 90 Loss

VE 90 270 GainNeither gain

+VE or VE = 90 or 270nor loss

11. Motion of the charged particle in magnetic

and electric fields.

Case I.

When , E and B

all the three are collinear..

In this case, the charged particle is moving parallel

or antiparallel to the fields, the magnetic force on

the charged particle is zero. The electric force

on the charged particle will produce acceleration.

qEa

m

As a result of electric force there will be

change in the speed of the charged particle along

the direction of the field. There will be no change

in the direction of motion of the charged particle

but speed, velocity, momentum and kinetic energy

will change.

Case II.

When , E and B

are mutually perpendicular

to each other.

If E & B

are such that, e mF F F 0,

then acceleration of the particle, F

a 0.m

It

means particle will pass through the fields without

any change in its velocity. Here

e mF F , So qE q B or E

B





This concept is used in velocity selector to get a

charged beam having a definite velocity.

12. A case of special interest is as follows :

E || B

i) In such a case e mF F

ii) Due to eF

, the test charge moves on a

parabolic path.

iii) Due to mF

, the test charge moves on a

circular path.

iv) The combined effect of both mF

and eF

is

to make the particle move along a parabolic

path in the plane of eF

and mF

.

(See the details below)

Fig. 12.1

v) Suppose, the test charge enters E

and B

at the origin of the co-ordinate axes, perpen-

dicular to both E

and B

.

vi) Let E & B

be along the Z-axis. And the

particle enters E & B

with velocity

along

the –VE direction of X-axis.

That is ˆE kE

ˆB kB

And i

vii) e 0ˆF kq E

& m 0 0ˆ ˆ ˆF q (i k) B jq B

viii) Acceleration of the test charge due to E

is

given by :

e 0z

F q Ea

m m

ix) The deflection of the test charge due to

electric field will be given by :

2

z

1z a t

2

where, t = time taken by the test charge to

go out of the electric and magnetic field. If

the field region exists over a distance , then

t

Hence,

22 0

z 2

q E1 1z a t

2 2 m

... (i)

x) Acceleration of the test charge due to B

will be given by :

0my

q BFa

m m

xi) Deflection of the test charge due to B will

be given by :

22 0

y 2

q B1 1y a t

2 2 m

or

2

0q B1y

2 m

... (ii)

From equation (i) and (ii) eliminating , we

find :

2 2 22 20 0q B q B1 1

y z z2 mE 2 mE

Thus the path of the particle is a parabola in

the yz-plane.

13. When E

is perpendicular to B

and particle

is fired with velocity

perpendicular to both

E

and B

. That is :

E B

i) Let E

be along Y-axis, B

be along the

Z-axis and velocity

be along the X-axis.

Fig. 15.1





ii) Then, e 0 0ˆF q E jq E

& m 0 0ˆF q B jq B

iii) e mF & F

are directed opposite to each other,,

hence they can cancel each other. In such

a case the test charge goes undeviated. For

such a case, we have

0 0q B q E

Hence, E

B

14. Galvanometers

Galvanometer is an instrument to detect

electric current. It can also be used to measure

potential difference or current strength by suitable

modification and calibration.

i) Types of galvanometers.

On the basis of principle of operation,

galvanometers are categorised as follows :

a) Moving magnet galvanometer.

Which operates on the basis of torque

acting on small permanent bar magnet due

to the magnetic field produced by the current

in a circular coil. In it magnet moves and

current carrying coil is stationary. Such a

galvanometer is also called moving iron type.

b) Moving coil galvanometer.

Which operates on the basis of torque

acting on a current carrying coil due to the

magnetic field of a permanent magnet. In it,

the current carrying coil moves and the

magnet is stationary.

Moving coil galvanometers are further

divided into two types, on the basis of

construction, as follows :

D' Arsonaval type galvanometer.

In it the coil is suspended from a

torsion head (support) with the help of a

phosphor bronze wire. The deflection is

noted with the lamp and scale arrangement.

It was designed by Kelvin and then modified

by D' Arsonaval.

Weston type galvanometer.

In it the coil is pivoted. The deflection

is noted with the help of a pointer and hence

it is also called pointer type galvanometer.

It was designed by Dr. Weston.

ii) The current through the moving coil galvano-

meter is given by :

cI

nAB ... (i)

where, c = torsional couple per unit

twist of the suspension wire, n = number of

turns, A = area of cross-section of the coil,

B = magnetic field in which the coil rotates

and = angle of deflection.

15. Current sensitivity of a moving coil galvano-

meter.

The deflection per unit current is called

current sensitivity of the galvanometer.

Suppose, a current I produces deflection in the galvanometer.

Then, current sensitivity is given by :

II

From equation (i), we find

1

nAB nAB or

I c c

Thus, current sensitivity of, the galvanometer

is directly proportional to the number of turns,

area of the coil and magnetic field in which the

coil is placed. Also, it is inversely proportional to

the torsional rigidity 'c' of the suspension wire.

In practice n and A cannot be increased

beyond a certain limit. So, to increase the current

sensitivity we make B as large as possible.

The 1 should be large for a good quality

galvanometer. In sensitive galvanometer quartz

fibre is used as a suspension wire for which c is

very small.

16. Voltage sensitivity

The deflection per unit potential difference or

voltage applied across the terminals of the

galvanometer is called voltage sensitivity.

If, be the deflection in the galvanometer

when the potential difference applied across it is

V, then voltage sensitivity is given by :

V

But V = IG where G is the resistance of the

galvanometer.





Hence we find :

1

1 q nAB

IG G G c

Thus, voltage sensitivity

1 Current sensitivity

Resistance

Voltage sensitivity depends upon the same factors

on which current sensitivity does.

17. Ammeter

Is an instrument for measuring current. It is a

low resistance galvanometer, so that its

inclusion in the circuit does not substantially

affect the current.

It is obtained from a galvanometer by connecting

a suitable shunt across the galvanometer.

Converting a galvanometer into ammeter.

Suppose, we wish to have an ammeter to

measure a current in the range 0 to I. Let G be

the resistance of the galvanometer and Ig be the

current that produces maximum possible

deflection in the galvanometer. Let S be the

resistance of the shunt. (See figure below).

When the current through the ammeter is I,

the current through the galvanometer should be

Ig, so that the deflection is maximum. When this

happens, the potential drop across the

galvanometer = potential drop across the shunt.

That is :

Fig. 17.1

g gI G (I I )S

This gives, g

g

IS G

I I

Thus, S can be calculated and the given

galvanometer can be converted into ammeter, by

connecting a shunt S across it.

18. Voltmeter

Is an instrument for measuring potential

difference. It is a high resistance galvanometer,

so that its inclusion in the circuit does not affect

the potential difference in the circuit. It is obtained

by connecting a high resistance in series with a

galvanometer.

Converting a galvanometer into a voltmeter.

Suppose, we wish to have a voltmeter to

measure potential difference in the range of 0 to

V. Let G be the resistance of the galvanometer

and Ig be the current that produces maximum

possible deflection in the galvanometer. We

connect a resistance R in series with the

galvanometer, so that when potential difference

across the combinations is V, the current through

the galvanometer is Ig. (See fig. below) Applying

Ohm's law we find : V = Ig (R + G). That is :

Fig. 18.1

g gV I G I R

This gives, g

g g

V I G VR G

I I

Thus, R can be calculated and given galvanometer

can be converted into a voltmeter by connecting

R in series with it.

19. Increasing the range of ammeter

Suppose, the resistance of an ammeter of

range I1 is G

A. Its range can be increased to I

2

by connecting a shunt S1 across it. The value of

S1 is given by,

11 A

2 1

IS G

I I

a) This process is similar to the conversion of

a galvanometer into ammeter.

Here Ig = I

1, G = G

A and I = I

2.

b) If 2 1I nI , then A

1

GS

n 1

.





20. Increasing the range of a voltmeter

Suppose the resistance of a voltmeter of

range V1 is G

. Its range can be increased to V

2

by connecting a resistance R1 in series with it.

The value of R1 is given by :

2 2 11

1 1

V V VR G G

(V / G ) V

a) Here Ig is equivalent to :

1V.

G

That is : 1g

VI

G

Also, the process is equivalent to the

conversion of a galvanometer into voltmeter

of range V2 and G = G

.

b) If 2 1V nV , then

1R (n 1)G .

21. Converting an ammeter into a voltmeter

Suppose, we have an ammeter of range I

and resistance GA. It can be converted into a

voltmeter of range V, by connecting a resistance

R in series with it. The value of R is given by :

A

VR G

I

22. Converting a voltmeter into ammeter

Suppose, we have a voltmeter of range V

and resistance G. To convert it into an ammeter

of range I, we need to connect a shunt S across

it. The value of shunt is given by :

VG

G VGS

I V IG V

G

23. Tangent Galvanometer

It is an instrument which can detect/measure

very small electric currents. It is also known as

moving magnet galvanometer. This galvanometer

is based on the tangent law.

Fig. 22.1

Magnetic field at the centre of the coil,

0NIB

2r

Where, N is the number of turns in the coil, I is

the current flowing through the coil, r is the radius

of the coil of galvanometer.

Now, 0H

NIB tan

2r

Or H H

0 0

2rB BI tan tan

N N / 2r

The quantity 0N

2r

is known as the galvanometer

constant G.

HBI tan

G

HB

G helps to reduce the deflection to

current I. So, this is known as reduction factor K

of the galvanometer.

Thus, I = K tan

That is, the electric current is proportional to the

tangent of the angle of deflection. That is why

this instrument is called tangent galvanometer.

Reduction factor of Tangent Galvanometer

(K) :

H

0

2rBK

N

K depends upon the geometry of the coil

and the value of horizontal component of earth's

magnetic field.

If = 450, then K = 1

That is, the reduction factor of a tangent

galvanometer is numerically equal to the current

required to produce a deflection of 450.

Sensitivity and accuracy of Tangent Galvano-

meter :

A tangent galvanometer is said to be

sensitive and accurate if for a given fractional

change in current, its deflection is large.

We know that, I K tan





Differentiating, we get,

2dI Ksec d

2

2

dI sec d cos d

I tan cos sin

d

sin cos

2d

sin 2

orsin 2 dI

d2 I

d will be maximum if sin 2 is maximum

i.e., 1. This is possible when 2 = 900.

or = 450

Therefore, the tangent galvanometer has

maximum sensitivity when the deflection is 450.





Magnetic Field

1. The magnetic field at the centre of the current

carrying coil :

a) is directed normal to the plane of coil

b) is directed parallel to the plane of the coil

c) is zero

d) has none of the above characteristics

2. An electron is fired parallel to uniform electric

and uniform magnetic fields acting simultaneously

and in the same direction. The electron :

a) gains energy

b) loses energy

c) moves along circular path

d) moves along a parabolic path

3. The magnetic field due to a current element is

independent of :

a) current through it

b) distance from it

c) its length d) none of the above

4. The unit of current element is :

a) Am–1 b) Am

c) Am2 d) Am–2

5. Magnetic field B on the axis of a circular coil far

away at distance x from the centre of the coil

are related as :

a) 3B x b)

2B x

c) 1B x d) none of the above

6. Two concentric coils carry the same current in

opposite directions. The diameter of the outer coil

is twice as compared to the inner coil. If at its

centre, the smaller coil produces a magnetic field

of 2 T, then, the magnetic field at the common

centres is :

a) 4 T b) 3 T

c) 2 T d) 1 T

7. An electron enter a region of space in which there

exist an electric field E and magnetic field B. If

the electron continues to move with the same

velocity in the same direction as before, which of

the following is NOT possible ?

a) E 0, B 0 b) E 0, B 0

c) E 0, B 0 d) E 0, B 0

MULTIPLE CHOICE QUESTIONS

8. A solenoid of 2.5 metre length and 2.0 cm diameter

possesses 10 turns per cm. A current of 0.5 ampere

is flowing through it. The magnetic induction at

axis inside the solenoid is :

a) 2 10–4 tesla b) 2 10–5 tesla

c) 2 10–6 tesla d) 2 10–7 tesla

9. A long wire carries a steady current. It is bent

into a circle of one turn and the magnetic field at

the centre of the coil is B. It is then bent into a

circular loop of n turns. The magnetic field at the

centre of the coil will be :

a) n B b) n2 B

c) 2 nB d) 2 n2B

10. What will be the value of the magnetic field

induction at the centre of the coil, if 1= 2 A,

h = 10 cm in the following figure ?

Fig. 10.1

a) 51.14 10 T

b) 5

0

41.14 10 T

c) 51.14

10 T4

d) 50 2.14 10 T

4

11. An infinite long straight wire is bent into a

semicircle of radius R, as shown in the figure. A

current I is sent through the conductor. The

magnetic field at the centre of the semicircle is :

Fig. 11.1

a) infinite b) zero

c) 0 I

4 R

d)

0 I( 1)

4 R

Magnetic Force

12. The torque acting on a magnetic dipole of moment

mP

when placed in a magnetic field B is :

a) pm B b) mP B

c) mP B

d) given by none of the above





13. A magnetic field exerts no force on :

a) stream of electrons

b) stream of proton

c) unmagnetised piece of iron

d) stationary charge

14. A current carrying coil is placed in an uniform

magnetic field, with its plane parallel to the

magnetic field. If the coil turns through angle ,

the torque and are related as :

a) sin b) cos

c) tan d) cot

15. A charge is fired through a magnetic field. The

force acting on it is maximum when the angle

between the direction of motion and magnetic

field is :

a) zero b) 4

c) 2

d)

16. The force on a current carrying conductor in a

magnetic field is maximum, when angle between

current and magnetic field is :

a) zero b) 4

c) 2

d)

3

4

17. No force is exerted by a magnetic field on a

stationary :

a) current loop

b) electric dipole

c) magnetic dipole

d) current carrying conductor

18. A straight wire 5 m long is placed parallel to an

infinitely long straight wire carrying current 5 A.

The distance between the two wires is 10 cm

and the 5 m long wire is carrying current 2 A.

The force on the shorter wire is :

a) 30 10 N

4

b) 103 N

c) 70 10 N

4

d) 10–7 N

Cyclotron

19. A cyclotron can be used to produce high energy :

a) -particle b) -particles

c) neutrons d) atoms

20. A cyclotron cannot be used to accelerate the :

a) protons b) ions

c) electrons d) -particles

21. What limits the energy that can be imparted to

charged particle in a cyclotron ?

a) Charge

b) Variation in mass with velocity

c) The gap between the dees

d) Some factor other than those mentioned above

22. A beam of a-particles having specific charge

2.5 107 C kg–1 moves with a speed of 2 105

m s–1 in a magnetic field of 0.05 T. What is

the radius of the circular path described by the

-particle ?

a) 4 cm b) 8 cm

c) 16 cm d) 32 cm

23. An -particle describes a circular path of radius

r in a magnetic field B. What will be the radius of

the circular path described by the proton of same

energy in the same magnetic field ?

a) r

2b) r

c) 2 d) 2 r

Galvanometer

24. Which one of the following is NOT the name of

a category of galvanometers ?

a) Moving coil b) Moving magnet

c) Moving field d) Moving iron

25. The ratio of earth's magnetic field and galvano-

meter constant for the tangent galvanometer is

called reduction factor because it reduces the :

a) magnetic field of earth

b) magnetic field of the coil

c) deflection of the magnet

d) tangent of deflection to current

26. To increase the range of a voltmeter we need to

connect a suitable :

a) high resistance in series

b) high resistance in parallel





c) low resistance in series

d) low resistance in parallel

27. To measure the resistance of a device using

Ohm's law, which of the following mode of

connection is used ?

a) Ammeter in series, voltmeter in parallel

b) Voltmeter in series, ammeter in parallel

c) Both ammeter and voltmeter in series

d) Both ammeter and voltmeter in parallel

28. Which of the following is correct statement ?

a) Ammeter is a high resistance galvanometer and

voltmeter is a low resistance galvanometer

b) Ammeter is a low resistance galvanometer and

voltmeter is a high resistance galvanometer

c) Ammeter and voltmeter cannot be distinguished

on the basis of their resistance

d) None of the above

29. The magnetic field in case of the moving coil

galvanometer should be radial so that current I

through the coil and its deflection are related to

each other as :

a) I tan b) I log

c) I d) I e

30. To increase the range of an ammeter, we need to

connect a suitable :

a) low resistance in parallel

b) low resistance in series

c) high resistance in parallel

d) high resistance in series

31. Why should the plane of the coil of tangent

galvanometer be parallel to the magnetic meridian?

a) To avoid the influence of earth's magnetic field

b) To increase the magnetic field due to the

current in the coil

c) To make earth's magnetic field perpendicular

to that due to the current in the coil

d) For some other reason

32. A galvanometer may be converted into ammeter

or a voltmeter. In which of the following cases

the resistance of the device so obtained will be

the largest ?

a) Ammeter of range 1 A

b) Ammeter of range 10 A

c) Voltmeter of range 1 V

d) Voltmeter of range 10 V

33. In the above question which device will have the

least resistance ?

a) Ammeter of range 1 A

b) Ammeter of range 10 A

c) Voltmeter of range 1 V

d) Voltmeter of range 10 V

34. On which of the following effects of current, is

the moving coil galvanometer based ?

a) Heating effect

b) Chemical effect

c) Magnetic effect

d) Thermoelectric effect

35. Which of the following relations is directly

applicable to the moving coil galvanometer ?

a) m

p B

b) 0B B tan

c) m 0F q B

d) none of the above

36. What is the relation between voltage sensitivity

and the current sensitive

1 of a moving coil

galvanometer ? Given that G is the resistance of

the galvanometer.

a) 1G b)

1

G

c) 1 G d) one of the above

37. The sensitivity of a moving coil galvanometer

increases with the decrease in :

a) number of turns b) area of coil

c) magnetic field d) none of the above

38. Best method to increase the sensitivity of the

moving coil galvanometer is to increase :

a) radius of the coil

b) number of turns of the coil

c) external magnetic field

d) none of the above

39. A voltmeter of range 3 V and resistance 200 cannot be converted to an ammeter of range :

a) 10 mA b) 100 mA

c) 1 A d) 10 A

40. In an ammeter 4% of the mains current is passing

through galvanometer. If the galvanometer is

shunted with a 5 resistance. What is the

resistance of the galvanometer ?

a) 4 b) 5

c) 20 d) 120





41. A galvanometer of resistance 100 gives full

scale deflection with 0.01 A current. How much

resistance should be connected in parallel with it

to convert it into an ammeter of range 10 A ?

Give the value up to 3 significant figures.

a) 0.100 b) 1.00

c) 10.0 d) none of the above

42. A voltmeter has resistance R0 and range V. What

resistance should be connected in series with it

to increase its range to nV ?

a) nR0

b) 0(n 1)R

c) 0(n 1)R d)

0R

n

43. To reduce the range of voltmeter, its resistance

need to be reduced. A voltmeter has resistance

R0 and range V. Which of the following resi tance

when connected in parallel will convert it into a

voltmeter of range V

?n

a) nR0

b) 0(n 1)R

c) 0(n 1)R d) none of these

44. An ammeter has resistance R0 and range I. What

resistance hould be connected in parallel with it

to increase its range to n ?

a) 0R

nb)

0R

(n 1)

c) 0R (n 1) d) none of the above

45. To decrease the range of an ammeter its resistance

need to be increased. An ammeter has resistance

R0 and range I. Which of the following resistance

can be connected In series with it to decrease its

range to I/n.

a) 0R

nb)

0R

(n 1)

c) 0R

(n 1) d) none of the above

46. When we shunt a galvanometer with a resistance

of 20 its deflection is reduced to half. What is

the resistance of the galvanometer ?

a) 80 b) 40

c) 20 d) 10

47. An ammeter is obtained by shunting a 30 galvanometer with a 30 resistance. What

additional shunt should be connected across it to

double its range ?

a) 10 b) 15

c) 30 d) none of the above

48. What resistance should be connected in series

with a 0.5. A ammeter to convert it into a 15 V

voltmeter. Given that the resistance of the ammeter

is 2 ?

a) 2 b) 5

c) 15 d) none of the above

49. A galvanometer gives full scale deflection when

the current passed through it is 1 mA. lts resistance

is 100 . Without shunting it, as such, it can be

used as an ammeter of range :

a) 1.000 A b) 0.100 A

c) 0.010 A d) 0.001 A

50. A galvanometer gives full scale deflection when

the current passed through it is 1 mA. Its resistance

is 100 . Without connecting additional resistance

in series with it, it can be used as a voltmeter of

range :

a) 1.000 V b) 0.100 V

c) 0.010 V d) 0.001 V

51. The sensitivity of a galvanometer is 60 divisions

per ampere. When a shunt is used its sensitivity

becomes 10 divisions per ampere. If the galvano-

meter is of 20 resistance, the value of the shunt

is :

a) 2 b) 4

c) 5 d) 8

52. An ammeter of range 100 mA has a resistance

of 2 ohm. What resistance should be connected

in series with it to use it as a voltmeter of range

1 volt ?

a) 8 b) 12

c) 16 d) 24

53. A galvanometer of resistance 200 ohm gives a

full scale deflection for a current of 10–3 ampere.

To convert it into an ammeter capable of measuring

upto one ampere, what resistance should be

connected in parallel with it ?

a) 2 10–6 ohm b) 2 10–3 ohm

c) 2 10–1 ohm d) 2 ohm





54. An ammeter A, a voltmeter V and a resistance

R are connected as shown in the figure. If the

voltmeter reading is 1.6 V and the ammeter

reading is 0.4 ampere then R is :

Fig. 54.1

a) Equal to 4 ohm

b) Equal to 5 ohm

c) Less than 4 ohm

d) Between 4 ohm and 5 ohm

55. If 10% of the main current is to the passed through

the moving coil galvanometer of resistance

99 ohm, then the required shunt resistance will

be :

a) 9.9 ohm b) 10 ohm

c) 11 ohm d) 9 ohm

56. A galvanometer of resistance 200 ohm gives full

scale deflection with 15 rnilli ampere current. In

order to convert it into a 15 volt range voltmeter,

the value of resistance connected in series is :

a) 800 ohm b) 1000 ohm

c) 1500 ohm d) 2500 ohm

57. A voltmeter of range 5 V is to be converted into

an ammeter of range 10 mA. If the resistance of

voltmeter is 1 k, then what resistance should

be connected in parallel with it ?

a) 0.2 k b) 0.5 k

c) 0.8 k d) 1.0 k

58. An ammeter of range 5 A is to be converted into

a voltmeter of range 10 V. If the resistance of

ammeter be 0.1 , then what resistance should

be converted in series with it ?

a) 1.1 b) 1.9

c) 2.1 d) 4.9

Recent Questions from MH-CET Exams.

59. When a galvanometer of resistance G is converted

into an ammeter of range IA then the current

passing through the galvanometer is given by :

a) g

SI I

S G

b) g

GI I

S G

c) g

S GI I

S

d) g

S GI I

G

60. A voltmeter has a resistance of G and a range

of V volts. The value of the resistance used in

series with it to convert it into voltmeter of range

nv volts is :

a) nG b) (n – 1) G

c) G

nd)

G1

n

61. Two tangent galvanometers are connected in

series and a current is passed through them. The

deflections recorded are 450 and 600. K1 and K

2

respectively are their reduction factors K1

: K2

is :

a) 1.732 : 1 b) 1.414 : 1

c) 1 : 2 d) 1 : 3

62. A tangent galvanometer is an instrument to

measure :

a) electric voltage

b) magnetic field

c) electric current

d) tangent of any geometrical angle

63. A wire of length L is bent into a circle and a current

I is passed through it. Next, the same wire is bent

into a coil of three turns and the same current is

passed through it. The magnetic induction at the

centre now, as compared to its value in the first

case is :

a) 1

9b)

1

3

c) Thrice d) Nine times

64. A moving coil galvanometer (sensitivity = 200

div/A) is connected in series with a tangent galv-

anometer. On passing a current, the galvanometer

shows a deflection of 15 divisions while the

tangent galvanometer shows a deflection of 450.

The reduction factor of tangent galvanometer is :

a) 7.5 10–3 A b) 7.5 10–4 A

c) 75 10–3 A d) 30 10–4 A

65. If 36 is resistance of galvanometer and 12 is resistance of combination of galvanometer and

shunt, the value of shunt is :

a) 16 b) 19

c) 18 d) 20





66. When 2 A current is passed through a tangent

galvanometer, it gives a deflection of 300. For 600

deflection, the current must be :

a) 1 A b) 2 3 A

c) 4 A d) 6 A

67. Accuracy of tangent galvanometer is maximum

for :

a) 450 b) 900

c) 00 d) 300

68. A voltmeter has a resistance of G ohm and range

V volt. The value of resistance used in series to

convert it into a voltmeter of range nV volt is :

a) nG b) G / n

c) (n 1)G d) G

n 1

69. The tangent galvanometers having coils of the

same radius are connected in series. Same current

flowing in them produces deflections of 600 and

450 respectively. The ratio of the number of tums

in the coil is :

a) 4

3b)

3 1

1

c) 3 1

3 1

d)

3

1

70. In ballistic galvanometer, the frame on which the

coil is wound is non-metallic to :

a) avoid the production of induced emf

b) avoid the production of eddy currents

c) increase the production of eddy currents

d) increase the production of induced emf

71. Which of the following is / are the units of strength

of magnetic field at a point ?

a) NA m–1 b) NAm

c) NA–1 m–1 d) NA–2 m–2

72. A wire of length L metre carrying current I ampere

is bent in the form of a circle. What is the magnitude

of magnetic dipole moment ?

a)

2IL

4b)

2 2I L

4

c)

2I L

8d)

2IL

8

73. The current sensitivity of moving coil galvanometer

is given by :

a) C

NIABb)

C

NAB

c) NAB

Cd)

NIAB

C

74. In an electron gun, electron accelerates through

a potential difference V. If the electron has charge

'e' and mass 'm then maximum velocity is :

a) 2V

mb)

m

e

V

c) 2eV

md) none of these

75. The difference in potential of 2 points lying on

the axis of a short bar magnet of moment 3 Am2

at the distance of 50 cms & 100 cms respectively

from its centre is :

a) 9 107 J/Am b) 8 10–7 J/Am

c) 9 10–7 J/Am d) 8 107 J/Am

76. The deflection in a moving coil galvanometer falls

from 50 divisions to 10 divisions, when a shunt of

12 is applied. The resistance of galvanometer

coil is :

a) 12 b) 24 c) 48 d) 50

77. Deflection of 450 produces current 173.2 mA in

a T.G., then how much current will give deflection

of 300 :

a) 10 mA b) 1 mA

c) 100 mA d) 173.2 mA

78. In a M.C.G., the sensitivity can be increased by :

a) increasing the effective area of coil

b) decreasing the magnetic field induction

c) decreasing the number of tums of coil

d) increasing the restoring torque per unit twist

79. For an ammeter, shunt resistance is given by :

a)R

Sn 1

in parallel

b)R

Sn 1

in series

c) S R(n 1) in parallel

d) S R(n 1) in series





80. A circular coil of 100 turns and cross-sectional

1 cm2 is wound to an inductor of 1 mH. If current

through the coil is 2 A, then, Bcentre

= ?

a) 0.2 T b) 0.4 T

c) 0.8 T d) 1 T

81. Sensitivity of moving coil galvanometer is increased

by 25%, then the number of turns is to be changed

from 28 to :

a) 24 b) 28

c) 35 d) 42

82. The current sensitivity of a galvanometer is x

div/mA and voltage sensitivity is y div/V. The

resistance of galvanometer is g. Then relation

between x and y is :

a) 3xG 10

y b)

yG

x

c) x

Gy

d) 3y G 10

83. Tangent galvanometer shows a deflection of 450

for some current. When the current is reduced

to 1

3 times the original, what is the deflection?

a) increases by 150 b) decreases by 150

c) increases by 300 d) decreases by 300

84. In order to convert a moving coil galvanometer

into a voltmeter ?

a) a high resistance is connected in parallel with

the galvanometer

b) a high resistance is connected in series with

the galvanometer

c) a low resistance is connected in parallel with

the galvanometer

d) a low resistance is connected in series with

the galvanometer

85. The tangent galvanometer is set into magnetic

meridian :

a) to rninirnise error due to parallax

b) to produce strong magnetic field

c) to make magnetic field due to current carrying

coil, exactly parallel to horizontal component

of earth's magnetic field.

d) to make magnetic field due to current carrying

coil, exactly perpendicular to horizontal com-

ponent of earth's magnetic field

86. Toroid is :

a) ring shaped closed solenoid

b) rectangular shaped solenoid

c) ring shaped open solenoid

d) square shaped solenoid

87. When a resistance of 100 is connected in series

with a galvanometer of resistance R, its range is

V. To double its range, a resistance of 1000 is

connected in series. Find R :

a) 700 b) 800

c) 900 d) 100

88. A voltmeter has a range O–V with a series

resistance R. With a series resistance 2 R its

range is O–V'. The correct relation between V

and V' is :

a) V' < 2 V b) V' > 2 V

c) V' = 2 V d) V' = V

89. The magnetic field inside a solenoid is :

a) directly proportional to its length

b) inversely proportional to the total number of

turns

c) inversely proportional to the current

d) directly proportional to the current

90. The sensitivity of a galvanometer is 60 divisions/

amp. When a shunt is used, its sensitivity becomes

10 divisions/amp. If galvanometer is of resistance

20 , the value of shunt used is :

a) 4 b) 5

c) 20 d) 8

91. In cyclotron, for a given magnet, radius of the

semicircle traced by positive ion is directly

proportional to :

[v = velocity of positive ion]

a) v–2 b) v–1

c) v d) v2

92. Magnetic induction produced at the centre of a

circular loop carrying current is. 'B'. The magnetic

moment of the loop of radius 'R' is :

[0 = permeability of free space]

a)

3

0

BR

3 b)

3

0

2 BR

c)

2

0

BR

2 d)

2

0

2 BR





93. Sensitivity of a moving coil galvanometer can be

increased by :

a) decreasing the number of turns of coil

b) increasing the number of turns of coil

c) decreasing the area of a coil

d) by using a weak magnet

94. A range of galvanometer is 'V', when 50 resis-

tance is connected in series. Its range gets doubled

when 500 resistance is connected in series.

Galvanometer resistance is :

a) 100 b) 200

c) 300 d) 400

REVISION OUESTIONS

from Competitive Exams

1. A current carrying coil is subjected to a uniform

magnetic field. The coil will orient so that its plane

becomes :

a) inclined at 450 to the magnetic field

b) inclined at any arbitrary angle to the magnetic

field

c) parallel to the magnetic field

d) perpendicular to the magnetic field

2. To convert a galvanometer into an ammeter, we

connect :

a) low resistance in series

b) low resistance in parallel

c) high resistance in series

d) high resistance in parallel

3. To convert a galvanometer of the moving coil type

into a voltmeter, we connect :

a) high resistance in series

b) high resistance in parallel

c) low resistance in series

d) low resistance in parallel

4. A current loop placed in a magnetic field behaves

like a :

a) magnetic dipole b) magnetic substance

c) magnetic pole d) all are true

5. The work done in turning a magnet of magnetic

moment 'M' by an angle of 900 from the meridian

is 'n' times the corresponding work done to turn it

through an angle of 600, where 'n' is given by :

a) 1 / 2 b) 2

c) 1 / 4 d) 1

6. A voltmeter has resistance of 2000 ohms and it

can measure upto 2 V. If we want to increase its

range to 10 V then required resistance in series

will be :

a) 2000 b) 4000

c) 6000 d) 8000

7. The resistance of a galvanometer is 2.5 and it

requires 50 mA for full deflection. The value of

the shunt resistance required to convert it into an

ammeter of 5 A is :

a) 2.5 10–2 b) 1.25 10–5

c) 0.05 d) 2.5





8. If only 2% of the main current is to be passed

through a galvanometer of resistance G then the

resistance of shunt will be :

a) G

50b)

G

49

c) 50 G d) 49 G

9. The resistance of an ideal voltmeter is :

a) zero b) very low

c) very large d) infinite

10. A galvanometer having a resistance of 8 ohm is

shunted by a wire of resistance 2 ohm. If the

total current is 1 ampere, the part of it passing

through the shunt will be :

a) 0.25 A b) 0.8 A

c) 0.2 A d) 0.5 A

11. We have a galvanometer of resistance 25 . It is

shunted by a 2.5 wire. The part of total current

that flows through the galvanometer is given as :

a) 0

I 1

I 11

b) 0

I 1

I 10

c) 0

I 3

I 11

d) 0

I 4

I 11

12. The coil of a moving coil galvanometer wound

over a metal frame in order to :

a) reduce hysteresis

b) provide electromagnetic damping

c) increase the moment of inertia

d) increase the sensitivity

13. Shunt required in an ammeter of resistance to

decrease its deflection from 30 ampere to 10

ampere is :

a) R

4b)

R

3

c) R

2d) R

[where, R is Resistance of ammeter]

14. A moving charge will produce :

a) only a magnetic field

b) only a electric field

c) both electric and magnetic field

d) none of the fields

15. An electron (mass = 9.0 10–31 kg and charge =

1.6 10–19 coulomb) is moving in a circular orbit

in a magnetic field of 1.0 10–4 Wb/m2. Its period

of revolution is :

Fig. 15.1

a) 3.5 10–7 second

b) 7.0 10–7 second

c) 1.05 10–6 second

d) 2.1 10–6 second

16. If in a moving coil galvanometer a current i

produces a deflection , then :

a) i tan b) 2i

c) i d) i

17. A rectangular loop carrying current 'I' is near a

long wire, also carrying current I as shown in

figure. The loop will :

a) rotate about an axis parallel to wire

b) move towards wire

c) remain stationary

d) move away from wire

18. A current of 2 ampere flows in a long, straight

wire of radius 2 mm. The intensity of magnetic

field at the axis of the wire is :

a) 30 10 tesla

b)

30 10 tesla2

c) 302

10 tesla

d) zero

19. The magnetic field at the centre of a circular coil

of radius r carrying current I is B1. The field at

the centre of another coil of radius 2 r carrying

same current I is B2. The ratio

1

2

B

B is :

a) 1

2b) 1

c) 2 d) 4





20. If in a circular coil A of radius R, current I is

flowing and in another coil B of radius 2 R a

current 2 I is flowing, then the ratio of the

magnetic fields, BA and B

B, produced by them

will be :

a) 1 b) 2

c) 1

2d) 4

21. If an electron and a proton having same momenta

enter perpendicular to a magnetic field, then :

a) curved path of electron and proton will be

same (ignoring the sense of revolution)

b) they will move undeflected

c) curved path of electron is more curved than

that of the proton

d) path of proton is more curved

22. If a current is passed through a spring then the

spring will :

a) expand b) compress

c) remain same d) none of these

23. When a charged particle enters in a uniform

magnetic field, its kinetic energy :

a) remains constant b) increases

c) decreases d) becomes zero

24. There are four voltmeters of the same range but

of resistances 10000 , 8000 and 4000 respectively. The best voltmeter among these is

the one whose resistance is :

a) 10000 b) 8000

c) 4000 d) all the equally good

e) none of the above

25. The magnetic field of given length of wire for

single turn coil at its centre is 'B', then its value

for two turns coil for the same wire is :

a) B

4b)

B

2

c) 4 B d) 2 B

26. A long solenoid carrying a current produces a

magnetic field B along its axis. If the current is

doubled and the number of turns per em is halved,

the new value of the magnetic field is :

a) B b) 2 B

c) 4 B d) B

2

27. A wire is wound in the form of a solenoid of length

and diameter d. When a strong current is passed

through the solenoid, there is tendency to :

a) keep both and d constant

b) decrease both and d

c) increase both and d

d) decrease but increase d

e) increase but decrease d

28. A wire of certain length carries a steady current.

It is first bent to form a circular of one turn. The

same wire is next bent to form a circular coil of

three turns. The ratio of magnetic inductions at

the centre of the coil in the two cases is :

a) 9 : 1 b) 1 : 9

c) 1 : 3 d) 3 : 1

e) 1 : 1

29. A proton and an -particle are projected normally

into a magnetic field. What will be the ratio of

the radii of the trjectories of the proton and particle ?

a) 2 : 1 b) 1 : 2

c) 4 : 1 d) 1 : 4

30. A long wire carries a steady current. It is bent

into a circle of one turn and the magnetic field at

the centre of the coil is B. It is then bent into a

circular loop of n turns. The magnetic field at the

coil will be :

a) n B b) n2 B

c) 2 n B d) 2 n2 B

31. The magnetic field due to a current carrying

circular loop of radius 3 cm at a point on the axis

at a distance of 4 cm from the centre is 54 T.

What will be its value at the centre of the loop ?

a) 250 T b) 150 T

c) 125 T d) 75 T

32. Two long conductors, separated by a distance d

carry currents I1 and I

2 in the same direction.

They exert a force F on each other. Now the

current in one of them is increased to two times

and its direction is reversed. The distance is also

increased to 3d. The net value of the force between

them is :

a) – 2 F b) F / 3

c) 2F

3 d)

F

3





33. Two parallel beams of positrons moving in the

same direction will :

a) repel each other

b) not interact with each other

c) attract each other

d) be deflected normal to the plane containing

the two beams

34. The maximum current that can be measured by

a galvanometer of resistance 40 is 10 mA. It

is converted into a voltmeter that can read upto

50 V. The resistance to be connected in series

with the galvanometer is ...... (in ohm) :

a) 2010 b) 4050

c) 5040 d) 4960

35. A proton a deutron and an alpha particle are

accelerated through same potential difference and

then they enter a normal uniform magnetic field.

The ratio of their kinetic energies will be :

a) 2 : 1 : 3

b) 1 : 1 : 2

c) 1 : 1 : 1

d) 1 : 2 : 4

36. A uniform electric field and a uniform magnetic

field are acting along the same direction in a

certain region. If an electron is projected in the

region such that its velocity is pointed along the

direction of fields. then the electron :

a) will turn towards right of direction of motion

b) speed will decrease

c) speed will increase

d) will turn towards left of direction of motion

37. Which of the field patterns given below is valid

for electric field as well as for magnetic field ?

a) b)

c) d)

38. A current carrying closed loop in the form of a

right angle isosceles triangle ABC is placed in a

uniform magnetic field acting along AB. If the

magnetic force on the arm BC is F

the force on

the arm AC is :

a) 2 F

b) F

c) F

d) 2 F

39. A long insulated copper wire is closely wound as

a spiral of N turns. The spiral has inner radius a

and outer radius b. The spiral lies in the X-Y plane

and a steady current I flows through the wire.

The Z-component of the magnetic field at the

centre of the spiral is :

a) 0NI b

In(b a) a

b) 0NI b a

In2(b a) b a

c) 0NI bIn

2b a

d) 0NI b a

In2b b a

40. Proton Deuteron and alpha particle of the same

kinetic energy are moving in circular trajectories

in a constant magnetic field. The radii of proton

deuteron and alpha particle are respectively rp.

rd and r

a. Which one of the following relation is

correct ?

a) d pr r r b) d pr r r

c) d pr r r d) d pr r r





41. A charge Q is uniformly distributed over the

surface of non-conducting disc of radius R. The

disc rotates about an axis perpendicular to its plane

and passing through its centre with an angular

velocity . As a result of this rotation a magnetic

field of induction B is obtained at the centre of

the disc. If we keep both the amount of charge

placed on the disc and its angular velocity to be

constant and vary the radius of the disc then the

variation of the magnetic induction at the centre

of the disc will be represented by the figure :

a) b)

c) d)

42. The coercivity of a small magnet where the

ferromagnet gets demagnetized is 3 103 Am–1.

The current required to be passed in a solenoid

of length 10 cm and number of turns 100, so that

the magnet gets demagnetized when inside the

solenoid is :

a) 30 mA b) 60 mA

c) 3 A d) 6 A

43. A closely wound solenoid of 2000 turns and area

of cross-section 1.5 10–4 m2 carries a current

of 2.0 A. It is suspended through its centre

and perpendicular to its length, allowing it to turn

in a horizontal plane in a uniform magnetic field

5 10–2 tesla making an anglet of 300 with the

axis of the solenoid. The torque on the solenoid

will be :

a) 3 10–3 Nm b) 1.5 10–3 Nm

c) 1.5 10–2 Nm d) 3 10–2 Nm

44. Two similar coils of radius R are lying concen-

trically with their planes at right angles to each

other. The currents flowing in them are I and 2 I

respectively. The resultant magnetic field

induction at the centre will be :

a) 03 I

2R

b)

0I

2R

c) 0I

R

d) 05 I

2R

45. A particle of mass M and positive charge Q,

moving with a constant velocity 1

1ˆu 4i ms ,

enters a region of uniform static magnetic field

normal to the x-y plane. The region of the magnetic

field extends from x = 0 to x = L for all values of

y. After passing through this region, the particle

emerges on the other side after 10 milliseconds

with a velocity 1

2ˆ ˆu 2( 3i j) ms .

The correct

statement(s) is (are) :

a) The direction of the magnetic field is –z direction

b) The direction of the magnetic field is +z direction

c) The magnitude of the magnetic field 50 M

3Q

units

d) The magnitude of the magnetic field is 100 M

3Q

units

46. A steady current I flows along an infinitely long

hollow cylindrical conductor of radius R. This

cylinder is placed coaxially inside an infinite

solenoid of radius 2 R. The solenoid has n turns

per unit length and carries a steady current I.

Consider a point P at a distance r from the common

axis. The correct statement(s) is (are) :

a) In the region 0 < r < R, the magnetic field is

non-zero

b) In the region R < r < 2R, the magnetic field is

along the common axis

c) In the region R < r < 2R, the magnetic field is

tangential to the circle of radius r, centered on

the axis

d) In the region r > 2R, the magnetic field is non-

zero

47. A current loop in a magnetic field :

a) can be in equilibrium in two orientations, both

the equilibrium states are unstable

b) can be in equilibrium in two orientations, one

stable while the other is unstable

c) experiences a torque whether the field is

uniform or non uniform in all orientations

d) can be in equilibrium in one orientation





48. Two identical long conducting wires AOB and

COD are placed at right angle to each other, with

one above other such that 'O' is their common

point for the two. The wires carry 1 and

2

currents, respectively. Point' P' is lying at distance

'd' from 'O' along a direction perpendicular to the

plane containing the wires. The magnetic field at

the point 'P' will be :

a) 2 2 1/ 20

1 2( )2 d

b)

0 1

22 d

c) 01 2

2 d

d)

2 201 2( )

2 d

49. A conductor lies along the z-axis at

1.5 z 1.5m and carries a fixed current of

10.0 A in za direction (see figure). For a field

B

= 3.0 10–4 0.2x

yˆe a T,

find the power

required to move the conductor at constant speed

to x = 2.0 m, y = 0 m in 5 10–3 s. Assume

parallel motion along the x-axis :

a) 1.57 W b) 2.97 W

c) 14.85 W d) 29.7 W

Paragraph for Questions (i) and (ii)

50. The figure shows a circular loop of radius a with

two long parallel wires (numbered 1 and 2) all in

the plane of the paper. The distance of each wire

from the centre of the loop is d. The loop and the

wires are carrying the same current I. The current

in the loop is in the counterclockwise direction if

seen from above.

i) When d a but wires are not touching the loop,

it is found that the net magnetic field on the axis

of the loop is zero at a height h above the loop. In

that case.

a) current in wire 1 and wire 2 is the direction

PQ and RS, respectively and h a

b) current in wire 1 and wire 2 is the direction

PQ and SR, respectively and h a

c) current in wire 1 and wire 2 is the direction

PQ and SR, respectively and h 1.2a

d) current in wire 1 and wire 2 is the direction

PQ and RS, respectively and h 1.2a

ii) Consider d >> a, and the loop is rotated about its

diameter parallel to the wires by 300 from the

position shown in the figure. If the currents in the

wires are in the opposite directions, the torque on

the loop at its new position will be :

[Assume that the net field due to the wires is

constant over the loop]

a)

2 2

0I a

d

b)

2 2

0I a

2d

c)

2 2

03 I a

d

d)

2 2

03 I a

2d

51. Two parallel wires in the plane of the paper are

distance X0 apart. A point charge is moving with

speed u between the wires in the same plane at a

distance X1 from one of the wires. When the wires

carry current of magnitude I in the same direction,

the radius of curvature of the path of the point

charge is R1. In contrast, if the currents I in the

two wires have directions opposite to each other,

the radius of curvature of the path is R2. If

0

1

X3,

X the value of 1

2

R

R is :

52. A galvanometer has a coil of resistance 100 ohm

and gives a full scale deflection for 30 mA current

If it is to work as a voltmeter of 30 volt range, the

resistance required to be added will be :

a) 900 b) 1800

c) 500 d) 1000

53. This question has Statement-I & Statement-II.

Of the four choices given after the Statements,

choose the one that best describes the two

Statements.





Statement-I : Higher the range, greater is the

resistance of ammeter.

Statement-Il : To increase the range of ammeter,

additional shunt needs to be used across it.

a) Statement-I is false, Statement-II is true

b) Statement-I is true, Statement-II is true,

Statement-II is the correct explanation of

Statement-I

c) Statement-I is true, Statement-II is true,

Statement-II is not the correct explanation of

Statement-I

d) Statement-I is true, Statement-II is false

54. In an ammeter 0.2% of main current passes through

the galvanometer. If resistance of galvanometer

is G, the resistance of ammeter will be :

a) 500

G499

b) 1

G499

c) 499

G500

d) 1

G500

55. A galvanometer gives full scale deflection with

0.006 A current. By connecting it to a 4990 resistance, it can be converted into a voltmeter

of range 0 – 30 V.

If connected to a 2n

249 resistance, it becomes

an ammeter of range 0 – 1.5 A. The value of n

is :

56. A wire carrying current I has the shape as shown

in adjoining figure. Linear parts of the wire are

very long and parallel to X-axis while semicircular

portion of radius R is lying in Y-Z plane. Magnetic

field at point O is :

a) 0 I ˆ ˆB ( i 2k)4 R

b) 0 I ˆ ˆB ( i 2k)4 R

c) 0 I ˆ ˆB ( i 2k)4 R

d) 0 I ˆ ˆB ( i 2k)4 R

57. An electron moving in a circular orbit of radius r

makes n rotations per second. The magnetic field

produced at the centre has magnitude :

a)

2

0n e

r

b)

0ne

2r

c) 0ne

2 r

d) zero

58. Two coaxial solenoids of different radii carry

current I in the same direction. Let 1F

be the

magnetic force on the inner solenoid due to the

outer one and 2F

be the magnetic force on the

outer solenoid due to the inner one. Then :

a) 1F

is radially inwards and 2F

= 0

b) 1F

is radially outwards and 2F

= 0

c) 1 2F F 0

d) 1F

is radially inwards and 2F

= 0 is radially

outwards

59. A proton and an alpha particle both enter a region

of uniform magnetic field B, moving at right angles

to the field B. If the radius of circular orbits for

both the particles is equal and the kinetic energy

acquired by proton is 1 MeV, the energy acquired

by the alpha particle will be :

a) 1.5 Mev b) 1 MeV

c) 4 MeV d) 0.5 MeV





Brain Teasers

1. Two co-axial wires one solid and one hollow, each

carry the same current I in opposite directions.

The radius of inner wire is r. The inner radius of

the hollow wire is r2 and the outer radius is r

3.

What is the magnetic induction at a distance r

from the axis, such that r2 < r < r

3 ?

a) 2 203

Ir r

2 r

b) 2 20

3 2

Ir r

2 r

c)

2 2

0 3

2 2

3 2

I r r

2 r r r

d) 0

2 2

3 2

I 1

2 r r r

2. In the above question what is the magnetic field

at a point where r < r1 ?

a) 0 1

2

Ir

2 r

b) 0

2

1

Ir

2 r

c) 0 I2

d)

2

0

2

1

Ir

2 r

3. Two circular coils 1 and 2 are made from same

wire but radius of 1st coil is twice that of 2nd coil.

What potential difference should be applied across

them so that the magnetic field at their centres is

the same ?

a) 2 b) 3

c) 4 d) 6

4. A plane spiral of N turns carries current I. The

turns are closely packed and the inner and outer

radii are a & b respectively. What is the magnetic

field at the centre of the spiral ?

a) 0 2 I

4 b a

b) 0e

2 I blog

4 b a a

c) 0e

b2 I log

4 a

d) 0 2 I

4

5. A circular coil of radius 7 m carries a current of

2 A. It is changed into a square. What is the

magnetic field at the centre of the coil in the two

cases ?

a) 0 0,

7 11

b) 0 0 4 2

, 7 11

c) 0 04 2,

11 7

d)

0 0, 11 7

6. Three long straight wires of same material are

connected to the same power supply in parallel.

The internal resistance of the power supply is

negligible. The lengths of the wires are same but

their areas of cross-section are in the ratio

3 : 4 : 5. What is the ratio of distances of 'middle

wire from the outerwires so that the net magnetic

force on it is zero ?

a) 3

5b)

5

3

c) 4

5d)

5

4

7. An electron moving with kinetic energy 6.6 10–14 J

enters a magnetic field 4 10–3 T at right angle

to it. The radius of its circular path will be nearest

to :

a) 25 cm b) 50 cm

c) 75 cm d) 1 m

8. A galvanometer of resistance 50 ohm is connected

to a battery of 3 volt alongwith a resistance of

2950 in series. A full scale deflection of 30

divisions is obtained in the galvanometer. In order

to reduce this deflection to 20 divisions, the

resistance in series should be :

a) 4450 ohm b) 5050 ohm

c) 5550 ohm d) 6050 ohm





GRAPHICAL BANK

9. The dots in Fig. 9.1 show magnetic field perpen-

dicular to the plane of the paper and coming out

of it. The curve ABC shows the trajectory of a

particle in the plane of the paper. What is the

particle ?

Fig. 9.1

a) Proton b) Electron

c) Neutron d) It cannot be predicted

10. A wire abe is carrying current I. It is bent as

shown in the figure and is placed in a uniform

magnetic field B. Length ab = and abc = 450.

What is the ratio of force on bc to that on ab ?

Fig. 10.1

a) 2 b) 1

2

c) 1 d) 3

2

11. What is the magnetic field at O due to current in

the infinite wire forming a loop as shown in the

figure ?

Fig. 11.1

a)0

1 2

I[cos cos ]

4 d

b)0

1 2

I[sin sin ]

4 d

c)0 2I

4 d

d)

0 I

4 d

12. What is the magnetic field at the centre C of the

wire OCABO shown below ?

Fig. 12.1

a) 0 I

4 x

b)

0 I

4 x

c) 0 I

( 1)4 x

d)

0 I( 1)

4 x

13. What is the magnetic field at the common centre

of the wire circuit (continuous line) as shown in

the figure below ?

Fig. 13.1

a) 0

1 2

I 1 1

8 R R

b)

0

1 2

I 3 1

8 R R

c) 0

1 2

I 1 3

8 R R

d)

0

1 2

I 3 1

8 R R

14. An infinitely long wire is bent in the form of a

semicircle at the end as shown in the figure. It

carries current I along a b c d o. If radius of the

semicircle be R, then what is the magnetic field

at the centre of the circular part :

Fig. 14.1

a) 0 2I

( 1)4 R

b)

0 2I( 1)

4 R

c) 0 I

( 1)4 R

d)

0 I( 1)

4 R





15. What is the magnetic field at the centre of

semicircle shown in the figure below :

Fig. 15.1

a) 0 2I

( 1)4 R

b)

0 2I( 1)

4 R

c) 0 I

( 1)4 R

d)

0 I( 1)

4 R

16. An infinite wire bent in the form of L carries

current I. What is the magnetic field at the point

O ?

Fig. 16.1

a) zero b) 0 I

4 2d

c) 0 I

4 d

d)

0 2I

4 d

17. An infinite straight conductor carrying current 2 I

is split into a loop of radius r as shown in the

figure. The magnetic field at the centre of the

coil is :

Fig. 17.1

a) 0 2( 1)

4 r

b) 0 2( 1)

4 r

c) 0 ( 1)

4 r

d) zero

18. A circular coil carries current I. An insulated

infinitely long wire placed along the diameter of

the coil is also carrying current I. The magnetic

force on the wire is :

Fig. 18.1

a) zero

b) along the wire

c) perpendicular to the wire and the plane of the

coil

d) perpendicular to the wire and in the plane of

the coil

19. A wire loop consists of two parts as shown Fig.

19.1.

Fig. 19.1

It is placed in a magnetic field directed into

the plane of the paper and increases with time.

Which of the following shows the induced current

correctly ?

a) b)

c) d)

20. Figure below shows two coils made from the

same wire and of radii a and b as shown below.

They are placed in a magnetic field perpendicular

to their plane which varies as B = B0 sin t. If

the resistance of the two coils be R, then what is

current in the loop ?





Fig. 20.1

a)0B cos t

R

b)

2 2

0

(a b )B cos t

R

c)

2 2

0

(a b )B cos t

R

d)

2 2(a b )cos t

R

21. Figures below show four ways of making a regular

hexagon out of wires of two different kinds P, Q.

With current leads at the middle of two opposite

wires, the magnetic field at the centre of the

hexagon is not zero in :

Fig. 21.1

a) case 1 only

b) cases 1 and 2 only

c) case 3 only

d) cases 3 and 4 only

22. A bar magnet with its length vertical, is held at

some height from a flat horizontal coil. The magnet

is dropped, generating an emf in the coil. The E

versus time t curve rest to reality is :

a) b)

c) d)

23. Figure below shows three configurations of

current and an observation point P. Values of i

and r are the same in all cases. The straight

portions extend to infinity and the curved ones

are circular. The magnetic induction at P in the

cases a, b and c have the ratio :

Fig. 23.1

a) 1 : 1 : 1

b)3

1 : (1 ) : 4

c)3

1 : (1 ) : 4

d)3

1 : (1 ) : 14

24. The magnetic field at the centre of one loop of a

circular wire of radius r carrying current i may

be taken as B0. If a particle of charge q passes

the centre of a semicircular wire, as shown below,

along the axis of the wire, the force on it due to

the current (with V as the particle speed) is :

Fig. 24.1

a) zero b) 0

1qB V

2

c) 0

1qB V

4

d) qB0V

25. The ammeter has range 1 ampere without shunt.The range can be varied by using different shuntresistances. The graph between shunt resistanceand range will have the nature :

Fig. 25.1





a) P b) Q

c) R d) S

26. An ammeter A, a voltmeter V and a resistance

R are connected as shown in the figure. If the

voltmeter reading is 1.6 volt and the ammeter

reading is 0.4 ampere then R is :

Fig. 26.1

a) Equal to 4 ohm

b) Greater than 4 ohm

c) Less than 4 ohm

d) Between 3 ohm and 4 ohm

01. (c)

02. (b)

03. (c)

04. (b)

09. (a)

10. (c)

11. (a)

12. (c)

17. (d)

18. (d)

19. (d)

20. (b)

Answer Key

MH Text Book Based MCQ's

01. (a)

02. (b)

03. (d)

04. (b)

05. (a)

06. (d)

07. (b,d)

08. (a)

09. (b)

10. (a)

11. (c)

12. (b)

13. (d)

14. (a)

15. (c)

16. (c)

17. (b)

18. (a)

19. (a)

20. (c)

21. (b)

22. (c)

23. (a)

24. (c)

25. (d)

26. (a)

27. (a)

28. (b)

29. (c)

30. (a)

31. (c)

32. (d)

33. (b)

34. (c)

35. (a)

36. (b)

37. (d)

38. (c)

39. (a)

40. (d)

41. (a)

42. (c)

43. (d)

44. (b)

45. (d)

46. (c)

47. (b)

48. (d)

49. (d)

50. (b)

51. (b)

52. (a)

53. (c)

54. (c)

55. (c)

56. (a)

57. (d)

58. (b)

59. (a)

60. (b)

61. (a)

62. (c)

63. (d)

64. (c)

65. (c)

66. (d)

67. (a)

68. (c)

69. (d)

70. (b)

71. (c)

72. (a)

73. (c)

74. (c)

75. (c)

76. (c)

77. (c)

78. (a)

79. (a)

80. (a)

81. (c)

82. (a)

83. (b)

84. (b)

85. (d)

86. (a)

87. (c)

88. (a)

89. (d)

90. (a)

91. (c)

92. (b)

93. (b)

94. (d)

REVISION QUESTIONS from Competitive Exams.

01. (d)

02. (b)

03. (a)

04. (a)

05. (b)

06. (d)

07. (a)

08. (b)

09. (d)

10. (b)

11. (a)

12. (d)

13. (c)

14. (c)

15. (a)

16. (c)

17. (b)

18. (d)

19. (c)

20. (a)

21. (a)

22. (b)

23. (a)

24. (a)

25. (d)

26. (a)

27. (a)

28. (b)

29. (b)

30. (b)

31. (a)

32. (c)

33. (c)

34. (d)

35. (b)

36. (b)

37. (c)

38. (b)

39. (a)

40. (c)

41. (b)

42. (c)

43. (c)

44. (d)

45. (a,c)

46. (a,d)

47. (b)

48. (a)

49. (b)

50. [(i)c, (ii)b]

51. (3)

52. (a)

53. (a)

54. (d)

55. (5)

56. (a)

57. (b)

58. (c)

59. (b)

BRAIN TEASERS

05. (b)

06. (a)

07. (b)

08. (a)

13. (b)

14. (c)

15. (c)

16. (a)

21. (d)

22. (d)

23. (b)

24. (a)

25. (b)

26. (b)




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Magnetic Effet of Electric Current

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