1
Physics 435, Homework #8
Due: Friday, March 17, 2017
Reading: Griffiths, Chapter 5.15.3.
1. Thomsons experiment to measure q/m of electron. In 1897, J. J. Thomson discovered the electron by
measuring the charge-to-mass ratio of cathode rays (actually, s

1
Physics 435, Homework #1
Due: 10am, Friday January 27, 2017
Reading: Griffiths, Chapter 2.12.2.
1. Calculating an electric field from a charge density using Gausss law. A total charge Q is distributed
as a spherically symmetric charge density given by
r

1
Physics 405, Homework #2
Due: Friday, February 3, 2017, 10am
1. A uniformly charged sphere Consider a uniformly charged solid sphere of radius R and total charge Q.
Calculate:
a) The electric field inside and outside the sphere.
b) The potential inside

Physics 435
Spring 2010
Homework #11
1) Consider a resistor built out a cylinder of radius r which carries a current I .
The material has a conductivity of 1 over the length l1 followed by a material
with a conductivity 2 over the length l 2 . Answer all

Physics 435
Spring 2014
Homework #7
1) An infinite line of charge with a free linear charge density of passes through
the center of a dielectric in the form of a thick cylindrical shell of inner radius
a and outer radius b . This dielectric has a position

Physics 435
Fall 2010
Homework #3
1. Griffiths problem 2.21
q
; Now for V ( r < R ) Begin w/ E by Gauss's Law:
V (r > R) =
4 0 r
0 4 r 2 Er =
4 r 3
r
q
qr
r
;E=
r =
r =
r
3
3
3 0
4 0 R 3
4 R / 3 3 0
q
R
V ( R ) - V ( r ) = - Er dr =
r
V (r ) = V ( R

Physics 435
Fall 2013
Homework #6
1) Write the first 2 non-vanishing terms for the r > R potential due to a charge
distribution of the form = + k for 0 < < / 2 and = k for / 2 < <
2l + 1
2l + 1 1
% l =
( ) Pl ( ) sin d =
(u )Pl ( u ) du where u = cos

Physics 435
Fall 2010
Homework #5
1. A long, conducting cylindrical shell of length L and radius R has a charge
of Q. The cylinder is centered with its central axis along the z-axis. Find
the total repulsive force that the half cylinder with x < 0 exerts

Physics 435
Fall 2010
Homework #4
1. Griffiths problem 2.39
Put on inside and - on outside. Es =
b ds
b
; V =
ln
=
2 0 s
2 0 a s 2 0 a
2 0
Q
C
=
=
V V
ln b / a
2. A battery supplies a constant potential of V. At time t=0 the switch is
closed and the ul

Physics 435
Fall 2010
Homework #9
r
1) Consider a surface current of the form K = k s on the z=0 plane and a thin
annulus in the region a < s < a + .
a) Calculate the total current flowing into and out of the annulus and use
these currents to compute Q /

1
Physics 435, Homework #3
Due: Friday, February 10, 2017, 10am
Reading: Griffiths, Chapter 2.42.5, 3.1
1. Fields in and outside a conductor containing cavities with charges. Two spherical cavities of radii a
and b are hollowed out from the interior of a

1
Physics 435, Homework #4
Due: Friday, February 17, 2017 10am
Reading: Griffiths, Chapter 3.13.3.
1. Boundary conditions and separable solutions of Laplaces equation in Cartesian coordinates. A
cubical box (sides of length a) consists of five metal plate

1
Physics 435, Homework #14
Due: Wednesday May 3, 2017
Reading: Griffiths, Chapter 9.1-9.3.
direction has an electric field
1. Polarization An electromagnetic wave polarized in the x
~ = E0 cos(kz t + )
E
x
polarized wave and a y
polarized wave
a) Cons

1
Physics 435, Homework #9
Due: Friday, March 31, 2017 10am
Reading: Griffiths, Chapter 5.3-5.4.
1. Magnetic field of concentric solenoids. Two long coaxial solenoids each carry current I, but in opposite
directions. The inner solenoid, of radius a, has n

1
Physics 435, Homework #12
Due: Friday April 21, 2017
Reading: Griffiths, Chapter 7.2.
1. Finding induced emf and current.
~
a) A long solenoid, of radius a, is driven by an alternating current, so that the field inside is sinusoidal: B(t)
=
B0 cos(t)
z

1
Physics 435, Homework #10
Due: Friday, April 7, 2017
Reading: Griffiths, Chapter 6.
1. Forces and torques on magnetic dipoles. Griffiths Problem 6.1. Calculate the torque exerted on the square
loop shown in Fig. 6.6, due to the circular loop (assume r i

1
Physics 435, Homework #11
Due: Friday April 14, 2017
Reading: Griffiths, Chapter 7.1 - 7.1.
1. Magnetic flux and electromotive force. A square loop of wire (side a) lies on a table, a distance s from a
very long straight wire, which carries a current I.

1
Physics 435, Homework #13
Due: Friday April 28, 2017
Reading: Griffiths, Chapter 7.3, 9.1.
1. Magnitude of the fields Just to get a feeling for the numbers: The electric field amplitude of an electromagnetic
wave in vacuum is E0 = 103 V/m (not a very st

1
Physics 435, Homework #7
Due: March 10, 2017 10am
Reading: Griffiths, Chapter 4.4.
1. Energy of a charged conducting sphere surrounded by a dielectric. A conducting sphere of radius
R1 carrying
R R R charge Q is surrounded by a linear dielectric of susc

1
Physics 435, Homework #6
Due: Friday, March 3, 2017
Reading: Griffiths, Chapter 4.14.4.
1. Electric field of a uniformly polarized spherical shell. A spherical shell with inner radius R and outer
radius 3R is filled with material that has constant polar

1
Physics 435, Homework #5
Due: Friday, February 24, 2017, 10AM
Reading: Griffiths, Chapter 3.24.1.
1. Legendre polynomials as the separable solutions to Laplaces equation for the polar angle in
spherical coordinates; Orthogonal functions.
a) Derive P3 (x

Physics 435
Fall 2010
Homework #8
1) A current carrying coil is in the form of an n-sided polygon which is inscribed
within a circle of radius a so that all n corners lie on the circle. Find the ratio
of the B-field in the center of the polygon to the B-f

Physics 435
Spring 2014
Homework #7
1) An infinite line of charge with a free linear charge density of passes through
the center of a dielectric in the form of a thick cylindrical shell of inner radius
a and outer radius b . This dielectric has a position

Physics 435
Fall 2010
Homework #3
1. Griffiths problem 2.21
2. Griffiths problem 2.35
3. Calculate the energy stored in charged sphere of radius R with a charge
density which grows as ( r ) r n up to R and is zero for r > R. Let Q be
the total charge cont

Jim Wiss
Extra Midterm 1 Review Problems
r
d
y
x
+
1. Consider two infinitely long, charged cylinders with central axes parallel to the z direction. Both
r
cylinders have a radius R. Their centers are offset by a vector d in the x-y plane of the paper
as

Midterm 2 Review
The potential for a solid, ungrounded, conducting sphere of radius R in an
G
A
R3
external electrical field E = E0 z is given by V ( r > R ) = E0 cos r 2 . This is
r
r
slightly modified from the form given in lecture. Answer all parts o

Physics 435
Fall 2010
Homework #1
1) A thin ring of charge of radius R lies in the x-y plane and is centered on the zaxis. Unlike the example worked out in lecture, the linear charge density on
r
the ring depends on according to = 0 (1 + cos ) . Find E( z

Physics 435
Fall 2010
Homework #1
1) A thin ring of charge of radius R lies in the x-y plane and is centered on the zaxis. Unlike the example worked out in lecture, the linear charge density on
G
the ring depends on according to = 0 (1 + cos ) . Find E( z

EM hw5
October 3, 2016
1
choose suitable coordinate and solve for laplacian
there is no charge inside the rectangular box, laplacian:
2
2
2
(~
x) = 0 ( 2 + 2 + 2 )(x, y, z) = 0
x
y
z
2
(1)
separate variables:
(x, y, z) = X(x)Y(y)Z(z)
(2)
1 2 X(x) 1 2 Y(y

Phys 435
Problem Set #4
Solutions
23 September 2016
Before we start anything, let us calculate the squared distance r2 from a point at (r, , )
to a point at (a, 0, 0) where spherical coordinates are used. Geometrically, one can see that
this distance is
r