Moving charges make magnetic fields
Magnetic fields affect moving charges
Electric and magnetic fields depend on reference frame
Change reference frame:
magnetic field is converted into electric
Ex' Ex Ey
'Ey vBz
1 v2 / c2 Ez
'Ez vBy
1 v2 / c2
Time varying magnetic field can produce electric field!
(magnetic induction)
Electric and Magnetic Fields
Electric and magnetic fields are interconnected
Solenoid: insided
NIB 0
outside 0B
Constant current: there will be no forces
on charges outside (B=0, E=0)
What if current is not constant in time? Let B increase in time
E~1/r E~dB/dt
Non-Coulomb ENC !
Changing Magnetic Field
1. Coulomb electric field: produced by charges rr
qE ˆ
4
12
1
0
1
2. Non-Coulomb electric field:
using changing magnetic fieldrdt
BdE
1~ 1
1
Same effect on charges: 1221 EqF
Two Ways to Produce Electric Field
Field outside of solenoid
ENC causes current to
run along the ring
What is emf and I?
ldEemf NC
22 rENC
R
rEI NC 22
Driving Current by Changing B
Ring has resistance, R
ldEemf NC
22 rENC
1. Change radius r2 by a factor of 2.
2/1~ rENC
22 rLemf does not depend on radius of the ring!
2. One can easily show that emf will be the same for any circuit
surrounding the solenoid
Effect of the Ring Geometry
ldEemf NC
A
D
NC
D
C
NC
C
B
NC
B
A
NC ldEldEldEldEemf
=0 =0
D
C
NC
B
A
NC ldEldEemf
0emf for any path which does not
enclose the solenoid!
Round-Trip Not Encircling the Solenoid
Can observe experimentally:
I=emf/R ENC~emf
1. ENC~dB/dt
2. ENC~ cross-section of a solenoid
emfd
dtB1 r1
2
Quantitative Relationship Between B and EMF
emfd
dtB1 r1
2
2
11 rB - magnetic flux mag on the area encircled by the circuit
Magnetic flux on a small area A:
ABAnB ˆ
Definition of magnetic flux:
dABdAnBmagˆ
Magnetic Flux
dt
demf
mag
Faraday’s law cannot be derived from the
other fundamental principles we have studied
Formal version of Faraday’s law:
Sign: given by right hand rule Michael Faraday
(1791 - 1867)
Faraday’s Law
dt
demf
mag
mag B1 r12
Example:
B1 changes from 0.1 to 0.7 T
in 0.2 seconds; area=3 cm2.
emft
0.6 T 3 10 4 m2
0.2 s9 10 4 V
What is the ammeter reading? (resistance of ammeter+wire is 0.5 )
A 3108.1/ RemfI
A Circuit Surrounding a Solenoid
Each loop is subject to similar
magnetic field emf of loops
in series:
dt
dNemf
mag
The EMF for a Coil With Multiple Loops
Time varying B can be
produced by moving coil:
by moving magnet:
by rotating magnet:
(or coil)
Moving Coils or Magnets
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