Fisika Dasar II - EL

7/30/2019 Fisika Dasar II - EL

1/128

FISIKA DASAR II

Wahyu Widanarto

e-mail : [email protected]

Program Studi Elektronika, Fakultas Sains dan Teknik Unsoed

Jl. dr. Soeparno No. 61 Purwokerto


2/128

W. Widanarto Fisika Dasar IIW. Widanarto Fisika Dasar II 2

Materi Kuliah

1. Listrik : Muatan listrik, hukum Coulomb, medan listrik,kondensator, hukum Gauss, fluks listrik, potensial, kapasitor,dielektrik, dipol, arus listrik dan hambatannya, memuati danmelucuti kapasitor.

2. Kemagnetan : Gaya dalam medan magnet, medan magnetic,tesla, Gauss, qvxB, siklotron, spektograf massa, gaya

kemagnetan dan arus listrik, momen dipol.3. Medan magnetik karena pengaruh arus listrik : Biot dan

Savart, definisi ampere, hukum integral-garis ampere, fluksmagnetik.

4. Induksi elektromagnetik : induktans, arus bolak-balik dan

dayanya, untai RLC sederhana.


3/128

W. Widanarto Fisika Dasar IIW. Widanarto Fisika Dasar II

Muatan Listrik

3


4/128


Muatan Listrik dalam Atom

Berdasarkan Model Atom Bohr : elektron-elektron bermuatannegatif mengorbit pada kulit atom dalam lintasan tertentumengelilingi inti atom yang bermuatan positif.

Pada keadaan normal, muatan positif dan negatif dalamatom adalah sama. Pada keadaan ini atom merupakan atomneutral.

Atom yang kehilangan satu atau lebih elektron dan atomyang kelebihan elektron disebut dengan ion negatif ataupositif.

4


5/128


Charging object dengan induction

Klasifikasi material berdasarkan kemampuan elektron bergerakdalam material

Electrical conductors are materials in which some of theelectrons are free electrons that are not bound to atoms andcan move relatively freely through the material.

Electrical insulators are materials in which all electrons arebound to atoms and cannot move freely through thematerial.

Semiconductor

5


6/128


Charging object dengan induction

6

(a) A neutral metallic sphere, with equal numbers of positive and negative charges.

(b) The electrons on the neutral sphere are redistributed when a charged rubber rod is

placed near the sphere.

(c) When the sphere is grounded, some of its electrons leave through the ground wire.

(d) When the ground connection is removed, the sphere has excess positive charge that is

nonuniformly distributed.

(e) When the rod is removed, the remaining electrons redistribute uniformly and there is a

net uniform distribution of positive charge on the sphere.


7/128


Hukum Coulomb

Charles Coulomb (17361806) measured the magnitudes of the electric forces between

charged objects using the torsion balance.

7

From Coulombs experiments, we can generalize thefollowing properties of the electric force between twostationary charged particles.The electric force is inversely proportional to the square of the separation

r between the particles and directed along the line

joining them; is proportional to the product of the charges q1 and q2

on the two particles; is attractive if the charges are of opposite sign and

repulsive if the charges have the same sign; is a conservative force.


8/128


Bentuk Vektor dari Hukum Coulomb

The law expressed in vector form for the electric force exerted by a charge q1 on asecond charge q2, written F12, is

8

if four charges are present, then the resultant force exerted by particles 2, 3, and 4on particle 1 is


9/128


Contoh

9


10/128


Contoh

Consider three point charges located at the corners of a right triangle,

where q1 = q3 = 5.0 C, q2 =-2.0 C, and a = 0.10 m.

Find the resultant force exerted on q3

.

10

Vektor


11/128


Medan Listrik (E)

A small positive test charge q0 placed near an objectcarrying a much larger positivecharge Q experiences an electricfield E directed as shown.

11


12/128


Medan Listrik

(a) For a small enough test charge q0, the charge distribution on thesphere is undisturbed.

(b) When the test charge q0, is greater, the charge distribution on the

sphere is disturbed as the result of the proximity ofq0 .

12


13/128


Bentuk vektor medan listrik (E)

13

Medan listrik yang diakibatkan oleh muatan listrik yang terbatas :


14/128



15/128


Medan Listrik dari Distribusi Muatan Kontinyu

The electric field at P due to a continuous charge distribution is the vector sumof the fields E due to all the elements q of the charge distribution.

15


16/128


Rapat Muatan

16


17/128


Contoh

A rod of length l has a uniform positive charge per unit length and a total charge Q.Calculate the electric field ata point P that is located along the long axis of the rod and adistance a from one end.

17


18/128


Contoh

A ring of radius a carries a uniformly distributed positive total charge Q. Calculate theelectric field due to the ring ata point P lying a distance x from its center along thecentralaxis perpendicular to the plane of the ring

18


19/128


Garis-garis Medan Listrik

19

Electric field lines penetrating two surfaces. Themagnitude of the field is greater on surface A than onsurface B.


20/128


Penggambaran Medan Listrik

The lines must begin on a positive charge and terminate on a negative charge. In thecase of an excess of one type of charge, some lines will begin or end infinitely faraway.

The number of lines drawn leaving a positive charge or approaching a negativecharge is proportional to the magnitude of the charge.

No two field lines can cross.

20


21/128


Garis-garis Medan Listrik

21


22/128


Gerak partikel bermuatan dalam medan listrik

When a particle of charge q and mass m is placed in an electric field E, theelectric force exerted on the charge is qE. If this is the only force exerted onthe particle, it must be the net force and causes the particle to accelerateaccording to Newtons second law. Thus,

22


23/128


Contoh

A positive point charge q of mass m is released from rest in a uniform electricfield Edirected along thexaxis, as shown in Figure. Describe its motion.

23


24/128


Contoh

An electron enters the region of a uniform electric field as shown in Figure, with

vi= 3.00 x 106 m/s and E = 200 N/C. The horizontal length of the plates is l= 0.100 m.

a. Find the acceleration of the electron while it is in the electric field.

b. If the electron enters the field at time t=0, find the time at which it leaves the field.

c. If the vertical position of the electron as it enters the field is yi=0, what is its verticalposition when it leaves the field?

24


25/128

W. Widanarto Fisika Dasar II 25

Fluk Medan Listrik

Anggap medan listrik adalah uniform dalam besardan arah.

Garis-garis medan menembus permukaan luasan Asecara tegak lurus seperti terlihat dalam gambar.

Jumlah garis-garis per satuan luas adalahproporsional terhadap besarnya medan listrik

Jumlah total garis-garis medan yang menembuspermukaan sebanding dengan perkalian E dan A Perkalian tersebut dinamakan fluk medan listrik Dimensi fluk medan listrik N.m2/C


26/128


Fluk Medan Listrik


27/128


Fluk Medan Listrik

Sebuah element kecil dari luasan permukaan Ai

. Medan listrik membentuk sebuah sudut dengan vektor

luasan yang didefinisikan sebagai nomal dari elemenpermukaan.

Fluk dapat dihitung :

dot product of two vectors

Fl k M d Li ik


28/128


Fluk Medan Listrik

Label 1: garis medan listrik menembus luasan permukaan dari dalam ke luar dan 90, Fluk negatif. Fluk total yang menembus luasan permukaan sebanding dengan jumlah total garis

yeng meninggalkan luasan permukaan.

Fluk medan listrik untuk luasan tertutup:

H k G


29/128


Hukum Gauss

Fluk total yang menembus permukaan Gauss

atau

where q in represents the net charge inside the surface and E represents the electricfield at any point on the surface.

H k G


30/128

W. Widanarto Fisika Dasar II

Hukum Gauss

30

the net flux through any closed surface surrounding a point charge q is given byq/0 and is independent of the shape of that surface. the net electric flux through a closed surface that surrounds no charge is zero. the electric field due to many charges is the vector sum of the electric fields

produced by the individual charges.

Contoh


31/128


Contoh

Hitung medan listrik yang disebabkan oleh muatan titik yang terisolasi

31

Sebuah bola pejal dengan jejari a mempunyai rapat muatan volume dan membawamuatan positif total Q

Contoh


32/128


Contoh

32

Beda Potensial dan Potensial Listrik


33/128


Beda Potensial dan Potensial Listrik

33

Dividing the potential energy by the test charge gives a physical quantity that dependsonly on the source charge distribution. The potential energy per unit charge U/q0 isindependent of the value ofq0 and has a value at every point in an electric field. Thisquantity U/q0 is called the electric potential(or simply the potential) V. Thus, theelectric potential at any point in an electric field is

Beda Potensial


34/128


Beda Potensial

if the test charge is moved between two positionsA and B in an

electric field, the chargefield system experiences a change inpotentialenergy. The potential difference V = VB - VAbetween two points A and B in an electric field is defined as thechange in potential energy of the system when a test charge ismoved between the points divided by the test charge q0:

34

Energi Potensial Listrik


35/128


Energi Potensial Listrik

35

A system consisting of a negative charge and an electric field gains electric potentialenergy when the charge moves in the direction of the field.

Equipotential Surface


36/128


Equipotential Surface

A uniform electric field directed along the positivex axis. Point B is at alower electricpotential than pointA. Points B and C are at the same electric

potential.

36

Potensial Listrik Akibat Muatan Titik


37/128


Potensial Listrik Akibat Muatan Titik

the electric potential at a point located a distancer from the charge

At any point in space, the electric field dueto the point charge is

37

Energi Potensial Akibat Muatan Titik


38/128


Energi Potensial Akibat Muatan Titik

(a) If two point charges are separated by a distance r12, the

potential energy ofthe pair of charges is given by

38

(b) If charge q1 is removed, a potential exists at point Pdue to charge q2.

Soal Latihan


39/128


Potensial Listrik Akibat Distribusi Muatan Kontinyu


40/128


y

the electric potential is taken to be zero when pointP is infinitely far from the charge distribution

40

Soal Latihan


41/128


Kapasitasi dan Dielektrik


42/128


Kapasitansi


43/128


The capacitance C of a capacitor is defined as the ratio of the magnitude of thecharge on either conductor to the magnitude of the potential difference betweenthe conductors:

43

Kapasitansi Plat Sejajar


44/128


the capacitance of a parallel-plate capacitor is proportional to the area of its platesand inversely proportional to the plate separation

44


45/128


Soal Latihan


46/128


A solid cylindrical conductor of radius a and charge Q is coaxial with a cylindrical shell of

negligible thickness, radius b > a, and charge -Q. Find the capacitance of this cylindricalcapacitor if its length is l.

46

Rangkaian Pararel Kapasitor


47/128


Rangkaian Seri Kapasitor


48/128


Kapasitor dengan Dielektrik


49/128


A dielectric is a nonconducting material, such as rubber, glass, or waxed paper. When

a dielectric is inserted between the plates of a capacitor, the capacitance increases. If

the dielectric completely fills the space between the plates, the capacitance increases

by a dimensionless factor 1, which is called the dielectric constant of the material.The dielectric constant varies from one material to another.

49

Kapasitor dengan Dielektrik


50/128


Penggambaran Atomik dari Dielektrik


51/128


Contoh


52/128


Arus listrik dan Hambatannya


53/128


Tegangan, Arus dan Hambatan

Tegangan merupakan energi potensial dari sebuah sumber listrik yang tersimpan

dalam bentuk muatan listrik. Tegangan dapat dianggap sebagai gaya mendorongelektron melalui sebuah konduktor. Beda dalam tegangan pada dua ujung simpulpada rangkaian disebut dengan beda potensial.

A constant voltage source is called a DC Voltage with a voltage that variesperiodically with time is called an AC voltage

Arus Listrik


54/128


Arus

Merupakan aliran muatan listrik persatuan waktu. electrons flow from the negative (-ve)terminal to the positive (+ve) terminal of the supply.

54

Hambatan


55/128


A uniform conductor of length l and cross-sectional areaA. A potentialdifferenceV =Vb - Va maintained across the conductor sets up an electric field E, and this fieldproduces a current I that is proportional to the potential difference.

55

the magnitude of the current density in the wireas

BecauseJ = I/A

Hubungan V, I dan R

Th l ti hi b t V lt C t d R i t i DC l t i l i it


56/128


The relationship between Voltage, Current and Resistance in any DC electrical circuit wasfirstly discovered by the German physicist Georg Ohm, (1787 - 1854). Georg Ohm foundthat, at a constant temperature, the electrical current flowing through a fixed linearresistance is directly proportional to the voltage applied across it, and also inversely

proportional to the resistance. This relationship between the Voltage, Current andResistance forms the bases of Ohms Law and is shown below.

Contoh


57/128


Hukum Kirchoff I


58/128


Hukum Kirchoff II


59/128


Resistor/Hambatan dalam Rangkaian Seri dan Pararel


60/128


Rtotal = R1 + R2 + R3 + ..... Rn etc.

Contoh


61/128


Hitung hambatan ekuivalen dari rangkaian di bawah

Rangkaian Dasar


62/128


Circuit - a circuit is a closed loop conducting path in which an electrical current

flows. Path - a line of connecting elements or sources with no elements or sources

included more than once. Node - a node is a junction, connection or terminal within a circuit were two or

more circuit elements are connected or joined together giving a connection pointbetween two or more branches. A node is indicated by a dot.

Branch - a branch is a single or group of components such as resistors or asource which are connected between two nodes.

Loop - a loop is a simple closed path in a circuit in which no circuit element ornode is encountered more than once. Mesh - a mesh is a single open loop that does not have a closed path. No

components are inside a mesh. Components are connected in series if they carry the same current. Components are connected in parallel if the same voltage is across them.

Rangkaian Dasar


63/128


Hukum Kirchoff I dan II


64/128


Contoh

Tentukan arus yang mengalir pada R


65/128


Tentukan arus yang mengalir pada R3

65

Mesh Current Analysis / Loop Analysis


66/128


Mesh Current Analysis


67/128


These equations can be solved quite quickly by using a single mesh impedance matrix Z.Each element ON the principal diagonal will be "positive" and is the total impedanceof each mesh. Where as, each element OFF the principal diagonal will either be"zero" or "negative" and represents the circuit element connecting all the appropriatemeshes. This then gives us a matrix of:

67

Mesh Current Analysis


68/128


1. Label all the internal loops with circulating currents. (I1, I2, ...IL etc)

2. Write the [ L x 1 ] column matrix [ V ] giving the sum of all voltage sources ineach loop.

3. Write the [ L x L ] matrix, [ R ] for all the resistances in the circuit as follows;

R11

= the total resistance in the first loop.

Rnn = the total resistance in the Nth loop.

RJK = the resistance which directly joins loop J to Loop K.

4. Write the matrix or vector equation [V] = [R] x [I] where [I] is the list ofcurrents to be found.

68

Hukum Ohm untuk AC


69/128


Ilustrasi untuk kasus dimana reaktasi induktif lebih dominandibandingkan dg reaktasi kapasitif

Hubungan Euler


70/128


Fungsi trigonometri dapat dihubungkan dengan komplek eksponensial oleh Hubungan Euler

Dari hubungan di atas fungsi trigonometri dapat diekspresikan dlm bentuk eksponensial komplek

Kombinasi Pararel dari Impedansi


71/128


Respon Induktor Untuk Rangk. AC


72/128

W. Widanarto Fisika Dasar IIW. Widanarto 72

Respon Kapasitif Dlm Rangk. AC


73/128


Respon Resistor Dlm Rangk. AC


74/128


Diagram Phasor


75/128

W. Widanarto Fisika Dasar IIW. Widanarto Fisika Dasar IIW. Widanarto 75

Impedansi Komplek Untuk RL dan RC


76/128


Rangk. Serial RLC


77/128


Resonansi dalam rangkaian RLC seri


78/128


Daya sebagai fungsi frekuensi untuk rangkaianRLC seri


79/128


Arus dan daya pada keadaan resonansi


80/128


Rangk. Pararel RLC


81/128



82/128



83/128


Motor


84/128


Generator


85/128


Generator dan Motor


86/128


Medan B dan Gaya FB Magnetik


87/128


Hasil Eksperiment Partikel yang bergerak dalam medan magnet:

Medan Magnetik


88/128


Gaya Magnetik


89/128


Satuan medan magnet

Pergerakan Elektron Dalam Medan Magnetik


90/128


Gaya Magnetik Pada Sebuah Kawat Konduktor


91/128



92/128



93/128



94/128


Torka pd loop arus dalam medan magnet uniform


95/128


a

b


96/128


IAxB

A= ab merupakan luas loop

Torka pada sebuah loop arus dalam medan magnetik uniform B

Momen dipole magnetik loop arus IA (A.m2)

Energi Potensial

Torka momen magnetik dalam medan magnetik


97/128


xB

BU

Energi potensial dari sistem dipol magnetik dalam medan megnetik tergantung pada orentasi dipol medanmegnetik


98/128


D`Arsonval Galvanometer


99/128


An end view of a DArsonval galvanometer. When the turnsof wire making up the coil carry a current, the magneticfield created by the magnet exerts on the coil a torque thatturns it (along with its attached pointer) against the spring.Show that the angle of deflection of the pointer is directlyproportional to the current in the coil.

Gerak partikel bermuatan dalam medan magnetik


100/128


Kecepatan sudut

Periode


101/128


Spektrometer massa


102/128


Untuk menentukan

Rasio m/q

Cyclotron


103/128


Efek Hall


104/128


Hukum Biot-Savart


105/128


Medan Magnet Pada Kawat Berarus


106/128


Aturan Tangan Kanan Untuk Menentukan Arah MedanMagnet


107/128


Medan Magnet Pada Loop Arus


108/128


Medan Magnet


109/128


Gaya Magnetik Diantara 2 Konduktor Pararel


110/128


Hukum Ampere


111/128


Hukum Ampere


112/128


Medan magnet yang dihasilkan kawat berarus


113/128


Medan magnet yang dihasilkan toroid berarus


114/128


Medan magnet yang dihasilkan lembaran arus


115/128


Medan Magnet Sebuah Solenoid


116/128


Fluk Magnetik


117/128


Hukum Gauss dalam Kemagnetan


118/128


Kemagnetan dalam materi


119/128


Induksi Elektromagnetik


120/128


Eksperiment Faraday


121/128


Hukum Faraday: Induksi

Hukum Faraday


122/128


Aplikasi Hukum Faraday


123/128


Electromotive Force (emf)


124/128


Induksi emf dalam sebuah konduktor bergerak


125/128


Hukum Lenz

Arus induksi dalam suatu loop akan muncul di dalam arah yang sedemikian rupa sehingga arah tersebutmenentang perubahan yang menghasilkannya


126/128


Hukum Faraday


127/128


Gelombang EM


128/128


Fisika Dasar II - EL

Documents

Transcript of Fisika Dasar II - EL