Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
Coulombs Law
NAME:
_
NAME:
_
NAME:
_
RECITATION SECTION:
_
INSTRUCTOR:
_
DATE:
_
This activity is based on the following concepts:
Charge is a fundamental property of matter, measured in coulombs (C).
There are two types of charges: positive and negativ
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
DC Circuits
NAME:
_
NAME:
_
NAME:
_
RECITATION SECTION:
_
INSTRUCTOR:
_
DATE:
_
This activity is based on the following concepts:
The power delivered by an EMF source is given by i.
The power dissipated by a single resistor is given by iV, where V is th
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 25: Electromagnetic waves
Griths: Section 9.2.1, 9.2.2
Travelling waves and the wave equation
Any function of the form f (k(x vt) describes a traveling wave. This is simply due to the fact that if we choose
a value of s = x vt, then x =
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 24: Energy in the magnetic eld, Maxwells term
Griths: Chapter 7
Energy stored in inductors
An external voltage source is used to provide the energy required to establish a magnetic eld in an inductor. The
rate at which work is done by t
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 23: Inductance and mutual inductance
Griths: Chapter 7
Microscopic origin of conductivity
Consider that we have a number density (number per unit volume), nq , of charged carriers which each have charge
q. Suppose that these charge carr
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 22: Current, current density, resistive materials
Griths: Chapter 7
The continuity equation
The current and current density are related through,
i=
j da =
dQ
dt
(1)
If we write,
Q=
(r)d
so that
iout =
dQ
=
dt
j da,
(2)
then,
d =
t
d
=
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 21: Faradays law  motional emf
Griths: Chapter 7
emf is called the electromotive force, but it is a voltage
There are many forces that can produce motion of the positive (holes) and negative (electrons) carriers in
conductors and semic
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 20: Calculating the magnetic vector and scalar potentials
Griths: Chapter 5
Calculating the vector potential
Recall that for the solenoid, we found that
A(s < R) =
0 nis
0 niR2
; A(s > R) =
2
2s
(1)
Outside the solenoid there is no magn
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 19: The vector potential, boundary conditions on A and B.
Griths: Chapter 5
The vector potential
In magnetostatics the magnetic eld is divergence free, and we have the vector identity ( F ) = 0 for any vector
function F , therefore if w
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 18: BiotSavart law, magnetic dipoles, vector potential
Griths: Chapter 5
BiotSavart law for innite wire
Amperes law is convenient for cases with high symmetry, but we need a dierent approach for cases where the
current carrying wire i
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 17: Magnets eld lines, North and South. Lorentz Force Law
Griths: Chapter 5
Magnetic poles and magnetic eld lines
There are many analogies between electrostatics and magnetostatics (time independent magnetic elds). Just as
there are two
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 16: Force between wires, Amperes law, F = il B
Griths: Chapter 5
Force between charged wires and between current carrying wires
Magnetostatics is the study of static magnetic elds and the direct currents (DC) that generate them. The MKS
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 15: Remarkable general properties of electrostatics
Griths: Chapter 3 Earnshaws theorem One of the remarkable aspects of Laplaces equation on any domain is that there can be no minima in the interior of the domain, there can only be sad
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 26: Dielectric materials
Griths: Chapter 4
Polarization at the atomic/molecular scale
To understand the broad aspects of dielectric materials and polarization, we rst look at two simple models of
atomic level polarization. These models
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 27: Dielectric materials
Griths: Chapter 4
General Relations
In dielectric materials, polarization leads to a reduction (screening) of applied electric elds so that the electric
eld inside the material is reduced as compared to vacuum.
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 28: Dielectric materials  problem solving
Griths: Chapter 4
Boundary value problems
The boundary conditions on the displacement eld and electric eld across a surface that has surface free charge
density f and surface bound charge densi
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
Magnetic Charge Transport
S. T. Bramwell
1
, S. R. Giblin2 , S. Calder1 , R. Aldus1 , D. Prabhakaran3 and T. Fennell4
arXiv:0907.0956v1 [condmat.other] 6 Jul 2009
1. London Centre for Nanotechnology and Department of Physics and Astronomy, University
Col
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Review sheet for Midterm 2
Griths: Chapters 5,7 and Sections 9.2.1, 9.2.2
Static magnetic elds: Static magnetic elds are generated by DC currents or by the intrinsic magnetic moment
of elementary particles. DC current in a wire is i = il, while
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Review sheet for Midterm 1
Griths: Chapters 13
Electric Field
There are two types of charge and they interact through Coulombs law F =
1
4
0
qQ
r2 r
=
1
4
0
qQ
r3 r.
The interaction
between many charges is found by using superposition. The ele
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
DC / RC Circuits
NAME:
_
NAME:
_
NAME:
_
RECITATION SECTION:
_
INSTRUCTOR:
_
DATE:
_
This activity is based on the following concepts:
DC Circuits:
o For resistances in series: the net resistance is equal to the sum of all resistances in
series:
Req R1 R
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
Review of dielectric and magnetic materials
Dielectric properties of materials are due to atomicscale electric dipoles. Atoms and molecules have induced dipoles
so that when an electric eld is applied they have a dipole moment. Often the response is li
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Midterm II (2009)
Time allowed 50 minutes. Do all questions  to get full credit you must show your working.
Problem 1. a) Write down the integral and dierential forms of Maxwells equations. b) Set the source terms in the
dierential forms to ze
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Midterm IB (2009)
Time allowed 50 minutes. Do all questions  to get full credit you must show your working.
The general solutions to Laplaces equation with two coordinates allowed to vary are:
V (x, y ) = (a + bx)(c + dy ) + k [A(k )cos(kx) +
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Midterm I (2009)
Time allowed 50 minutes. Do all questions  to get full credit you must show your working.
The general solutions to Laplaces equation with two coordinates allowed to vary are:
V (x, y ) = (a + bx)(c + dy ) + k [A(k )cos(kx) +
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 31: Some nal remarks
Griths: Chapters 4,6
Boundary value problems for magnetostatics with materials
The equations are,
H dl = if ;
B dl = 0 (if + ib );
B da = 0
(1)
so that the boundary conditions across a surface that may carry both fr
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 30: Magnetic materials
Griths: Chapter 6
Magnetostatics of materials
No applied current or external eld
The magnetostatics treatment of magnetic materials is based on the concept of the magnetic moment density or
magnetization M . The m
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 29: Magnetic materials
Griths: Chapter 6
Magnetic materials
Extension of Maxwells equations to treat magnetic elds inside and outside magnetic materials is achieved in
manner that in some ways is like the treatment of the dielectric res
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 14: Multipole expansion
Griths: Chapter 3
Expansion of 1/r r  (Legendres original derivation)
Consider a charge distribution (r ) that is conned to a nite volume . For positions r that are outside the
volume , we can nd the potential
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
1
PHY481  Lecture 12: Solutions to Laplaces equation
Griths: Chapter 3 Before going to the general formulation of solutions to Laplaces equations we will go through one more very important problem that can be solved with what we know, namely a conducting
Birla Institute of Technology & Science, Pilani  Hyderabad
Electricity and magnetism
PHY 481

Fall 2015
Faradays Law, Inductance, and RL Circuits
NAME:
_
NAME:
_
NAME:
_
RECITATION SECTION:
_
INSTRUCTOR:
_
DATE:
_
This activity is based on the following concepts:
Faraday's Law of Induction: If the magnetic flux B through a closed loop C changes
with time,