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
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 9
Solution
Due March 27, 2017
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
Due February 27, 2017
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 light (i.
PHYS 436 Homework 1 CHECKPOINT SHOW YOUR WORK!
#1) a) W =
Q2d
2 0 A
Q2d
b) W =
2 0 A
#2) a)
= j0 cos x
t
b) Hint: To know if charge is conserved, you must know the total charge in the system.
PHYS 436 Homework 2 CHECKPOINT SHOW YOUR WORK!
#1) In the absence of surface current, the perpendicular component of S is continuous.
qB0 c 2
S
(0, 0, sin )
=
#2) a)
(in spherical coordinates)
4 r 2
S =0
b) There is no net flow of energy
0
L=
L=
x
y
c)
PHYS 436 HW 7Solution
by Chun Kit Chan
March 12, 2012
Pro. 10.3 1
Problem
@A
rV
@t
@
1 qt
r
=
@t
40 r2
1 q
r
=
40 r2
E =
B = r A
1
1 @Ar 1
@Ar
=
+
r sin @
r
@
= 0
= 0 r E
r
q
=
r
4
r2
= q (r)
1
J =
0
rB
@E
0
@t
=0
Since B is continuous everywhere, th
PHYS 436 HW8 Solution
April 3, 2012
Pro. 11.11
Problem
Eqn. 11.12 says
V (r, , t) =
p0 cos
40 r
!
sin ! t
c
r
c
+
1
cos ! t
r
r
c
Eqn. 11.17 says
A(r, , t) =
0 p 0 !
sin ! t
4r
r
c
z
Thus,
@V
p0 cos
=
@t
40 r
!
cos ! t
c
r
c
1
sin ! t
r
r
c
an
PHYS 436 HW3 Solution
Chun Kit Chan
February 14, 2012
Pro. 9.7 1
Problem
(a) For a line segment
Then,
z with deformation f (z), the forces acting on it are
2
@ f
Frestoring = T 2
z
@z
@f
Fdissipation = Fdrag =
z
@t
@ 2f
Frestoring + Fdissipation = Ftot
PHYS 436 HW Solution
by Chun Kit Chan
March 2, 2012
Most of the values for the resistivity, conductivity and permittivity are taken from the wikipedia
and is taken to be approximately 0 . We should recognize that as those quantities vary a lot,
what is re
Physics 436
Homework 9
Due March 27, 2017
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 direction. Sho
Physics 436
Due March 6, 2017
Homework 7
1. Recall that the resonant TE modes in a rectangular box are mnl = c
( ) +( ) +( )
m
a
2
n
b
2
l
d
2
1
2 ,
where a, b, and d are the box dimensions. There are similar TM modes in the box.
a. Calculate the approxi
Physics 436
Homework 2
Due January 30, 2017
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 surface
Physics 436
Homework 4
Due February 13, 2017
1. Injection of light into an optical fiber.
source:&
shell:&ns#
Light from a source enters the end of a cylindrical fiber with
ni#
incident angle , as shown. The source has an index of
core:&nc#
i#
refraction
Physics 436
Homework 1
Due January 23, 2017
This is review.
Each problem is worth five points. In this course, all HW problems will be have the same value
unless stated otherwise.
1. Electrostatic energy.
Calculate the electrostatic energy in a parallel-p
Physics 436
Due February 6, 2017
Homework 3
Please look at the P435 introductory lectures on EM waves linked from the course syllabus page
if you need a refresher on EM waves.
1. Consider a plane wave traveling along z. The electric field is
! !
i
(
)
i
E
Physics 436
Homework 8
Due March 13, 2017
1. Consider the electric field of a point charge moving with constant velocity:
! !
R
1 2
q
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 = v/c. T
Physics 436
Homework 1
Solution
Due January 23, 2017
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
January 31, 2017
Discussion 3
Solution
1. Consider two quantities that have the same , but not necessarily the same amplitude and
phase: f! z,t = A! f e i t and g! z,t = A! ge i t . (The phase information is in the complexness of
A.) Show
PHYS 436 HW4 Solution
by Chun Kit Chan
February 22, 2012
Problem
1
Pro. 9.16
Here x-z plane is the plane of incidence, I , R and T are the angle of incidence,
reflection and transmission respectively and z is the normal of the boundary surface. The fields
PHYS 436 HW2 Solution
Chun Kit Chan
February 14, 2012
Pro. 8.71
Problem
The setting of the solenoid of this problem is given in Fig. 1
Figure 1: Setting of coordinates and parameters of the problem (Fig. 8.7 of Griths)
We let Is (s) be the current on the
Problem 1
(a) From the translational and rotational symmetry about z - axis, the vector potential A is
a function of s and t only. Thus (using the symbol R = r r0 and A (r, t) = A (s, t) here.)
0
A (s, t) = z
4
Now the current can be written as
1
1
I (tr
Physics 436
Due April 3, 2017
Homework 10
Solution
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
s
Physics 436
Due March 6, 2017
Homework 7
Solution
1. Recall that the resonant TE modes in a rectangular box are mnl = c
( ) +( ) +( )
m
a
2
n
b
2
l
d
2
1
2 ,
where a, b, and d are the box dimensions. There are similar TM modes in the box (see the
old HW6
Physics 436
Homework 11
Due April 10, 2017
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 lady named B
Physics 436
Due May 1, 2017
Homework 14
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 potential 4-vec
Physics 436
April 4, 2017
Discussion 11
Solution
Exam review:
1. A perfectly conducting rectangular cavity has sides a < b < c (x, y, and z respectively).
a. What is the smallest resonant frequency of this cavity?
b. Write the equations that describe E(x,
Physics 436
Discussion 10
Solution
1. Griffiths, 11.10.
An insulating circular ring (radius b) lies in the xy plane, centered
at the origin. At t = 0, it carries a linear charge density, = 0 sin .
The ring is now made to rotate about the z axis with angul
Physics 436
Due April 3, 2017
Homework 10
Exam review:
1. A fairly easy (I hope!) potential exam problem.
What fraction of dipole radiation is emitted within 45 of the equatorial plane?
2. Too obscure for an exam problem. This is similar to Griffiths prob
Physics 436
Discussion 14
Solution
April 25, 2017
1. Obtain the continuity equation (conservation of charge, j = 0 ) from Maxwells equations:
F = 0 J and G = 0 . (Would you have guessed that conservation of charge is built
into the equations?)
Differ
Physics 436
Homework 13
Due April 24, 2017
!
!
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 .
!
!
(
(
)
)
(
)
! E
!
2. Suppose ob
Physics 436
Discussion 13
Solution
April 18, 2017
1. E and B are vectors. Problem 4 of the old HW13 was to show that the behavior of F is
consistent with this. However, B is actually an axial, or pseudo vector. This means that its
behavior under coordinat
Physics 436
Discussion 12
Solution
April 11, 2017
1. This is Griffiths, 12.11 (p. 518).
A turntable of radius R rotates at angular velocity . The circumference is, presumably,
Lorentz contracted, but the radius (being perpendicular to the velocity) is not