Physics 436
Homework 1
Solution
Due January 25, 2016
This is review.
Each problem is worth five points. In this course, all HW problems will have the same value
unless stated otherwise.
1. Electrostatic energy.
Calculate the electrostatic energy in a para
Physics 436
Homework 13
Solution
Due April 25, 2016
!
!
1. Observer A measures E = ( a,0,0) and B = ac ,0, 2ac , where a is a constant.
!
!
!
Observer B (moving) measures E = E x ,a,0 and B = ac ,By , ac . Determine E x and By .
!
!
! !
Use the invariance
Physics 436
Homework 8
Solution
Due March 14, 2016
1. Consider the electric field of a point charge moving with constant velocity:
! !
q
1 2
R
E ( r ,t ) =
, where R is the vector from the present position of the
3/2
2
4 0
R2
1 ( sin )
!
charge to r and
Physics 436
Homework 3
Solution
Due February 8, 2016
Please look at the old HW3. Those problems are a useful review of mechanical waves, relevant
to this course. Also look at last semesters P435 introductory lectures on EM waves (linked from
the course sy
Physics 436
Homework 5
Solution
Due February 22, 2016
NOTE: The first exam is Wednesday, February 24, in class.
1. In discussion, you calculated the radiation pressure on a perfectly absorbing material.
a. Calculate the pressure on a perfectly
Physics 436
Homework 7
Solution
Due March 7, 2016
( ) ( ) ( )
1
2
2
2 2
1. Recall that the resonant TE modes in a rectangular box are mnl = c ma + nb + ld ,
where a, b, and d are the box dimensions. There are similar TM modes in the box (see the
old HW6
Physics 436
Homework 10
Solution
Due April 4, 2016
Exam review:
1. A fairly easy (I hope!) potential exam problem.
What fraction of dipole radiation is emitted within 45 of the equatorial plane?
Just take the ratio of these two integrals:
2
3 /4
0
/4
Physics 436
Homework 9
Solution
Due March 28, 2016
1. An electron with initial speed vi c approaches a distant repulsive Coulomb potential
!
Ze2
. The electron will travel in a straight line, decelerating until it stops and
PE(r) = +
4 0r
!
reverses direc
Physics 436
Homework 6
Solution
Due February 29, 2016
1. We saw in lecture that for the radial E, tangential B wave in a coaxial cable the current in
the center conductor (actually, in either conductor) equals the linear charge density times the
speed of
Physics 436
Homework 14
Solution
Due May 2, 2016
x"
1. Consider the parallel-plate capacitor shown.
The plates are infinite, so you dont need to
worry about fringe fields. The origin of the
coordinates is at the bottom (V = 0) plate.
a. What is the potent
Physics 436
Homework 12
Solution
(
Due April 18, 2016
(
)
)
!
!
1. Determine the Lorentz transformation w = w0 ,w w = w0 ,w of a 4-vector to a
!
!
v !
reverence frame moving in an arbitrary direction, = x , y , z . That is, observer O
!c
sees observer O m
Physics 436
Homework 4
Solution
Due February 15, 2016
source:&
shell:&ns#
1. Injection of light into an optical fiber.
n
i#
source:&core:&nc# shell:&ns#
Light from a source enters the end of a cylindrical fiber with
i#
ni#
incident angle , as shown. The s
Physics 436
Homework 2
Solution
Due February 1, 2016
Note: Problem 3 is worth 10 points.
1. Recall the boundary conditions on static E and B at an interface between two materials:
E !and!B are always continuous, and H! is continuous in the absence of free
Homework 7
Problem 1:
Use the definition B A , we can get magnetic field first:
x
B A0 sin kx t y x
0
E V
y
y
Ay
z
z x z Ay z x Ay kA0 cos kx t z
0
A
A0 sin kx t y A0 cos kx t y
t
t
This implies that
E
A0 cos kx t 0
y
B
kA0 cos kx t 0
z
x
E x
Homework 7
Problem 1:
Use the definition B A , we can get magnetic field first:
x
B A0 sin kx t y x
0
E V
y
y
Ay
z
z x z Ay z x Ay kA0 cos kx t z
0
A
A0 sin kx t y A0 cos kx t y
t
t
This implies that
E
A0 cos kx t 0
y
B
kA0 cos kx t 0
z
x
E x
Physics 436
Homework#4 solutions
Problem 9.2
2 f
f
Ak 2 sin(kz ) cos(kvt ) ;
Ak cos(kz ) cos(kvt ) ;
z 2
z
2 f
2 f
f
Ak 2v 2 sin(kz ) cos(kvt ) v 2 2
Akv sin(kz )sin(kvt ) ;
t 2
z
t
1
Using the trig identity sin cos [sin( ) sin( )] to write
2
A
cfw_si
Physics 436
Homework 11
Solution
Due April 11, 2016
There are three problems for credit, plus two math review problems (not for credit).
1. This is a rejoinder to Griffiths 12.22b (p. 532), reproduced here:
b. Consider this limerick:
There was a young lad