Physics 425, Spring 2012
Assignment set #1
Due Jan 18:
1. In this problem, you will study the boundary conditions of the
electric and magnetic fields. Suppose that we measure the
electric field and magnetic field across a surface dividing two
linear mater
Physics 425, Spring 2012
Assignment set #6
Due February 15:
13. In this problem, you will study wave dispersion in a dielectric
insulating media whose electric susceptibility E is a complex
function of the EM wave frequency as:
q2
1
E =
m 0 0 2 2 i
(
)
wh
Physics 425, Spring 2012
Assignment set #7
Due February 24:
16. The electromagnetic fields between two parallel conducting
E
E = E0e i( kzt ) x , B = 0 e i( kzt ) y . Now consider
plates are given as
c
that we roll the two plates into infinitely long co-a
Physics 425, Spring 2012
Assignment set #5
Due February 8:
10. Griffiths Problem 9.19
Due February 10:
11. Griffiths Problem 9.21
Due February 13:
12. Turn in the last part of Quiz 2: sunlight traveling from air is
normally incident upon a conducting surf
Physics 425, Spring 2012
Assignment set #4
Due Feb 1:
7. Griffiths Problem 9.35: note that you can use the conclusion of
the assignment Problem 6.
Due Feb 3:
8. Griffiths Problem 9.17
Due Feb 6:
9. Griffiths Problem 9.16
Physics 425, Spring 2012
Assignment set #2
Due January 20:
2. Suppose that the electric field in an electromagnetic wave is
E
E (r , t ) = 0 sin(kz t )( x y ) .
2
(a) Prove that this solution satisfies the wave equation.
(b) Find the magnetic field using
Physics 425, Spring 2012
Assignment set #3
Due January 25:
4. Circularly polarized waves: consider a superposition of waves
traveling in the z direction:
E (r , t ) = Re E0e i1 e i( kz t ) x + E0e i 2 e i( kz t ) y
[
(a) find B (r , t ) ;
]
(b) calculate
Physics 425, Spring 2012
Assignment set #8
Due February 29:
18. Griffiths 9.29
Due March 2:
19. Consider a wave guide with a rectangular cross section of
10cm x 5cm. Which TE modes can propagate for angular
frequency 4 GHz? What are the 5 lowest cutoff fr
Physics 425, Spring 2012:
Assignment set #9
Due March 7:
21. Griffiths 10.4
Due March 9:
22. From the class, we find the (approximate) potentials by an
electric dipole
P
as: V ( r , t ) =
1 rP
0 P
, A( r , t ) =
. Find the
4 0c r
4 r
electric and magneti
1
Solutions to Quiz 5
(a) Radiation by moving charges is proportional to a2 . For charges accelerated by the electromagnetic force, there is ma = q (E + v B ), or a 1/m, and a2 1/m2 . Therefore, the light
particles radiate more. Between protons and electr
1
Solutions to Quiz 6
(a) The particles proper time is shorter by a factor of u = 1/
u = 2/2c. In S frame, ux = 0, uy = 2/2c, and uz = 0.
1 u2 /c2 =
(b) We can rst calculate the velocity of the particle in the S frame. Here = 1/
u =
x
2. Therefore,
1 v 2
1
Solutions to Quiz 4
(a) The scalar potential is given by
V (r, t) =
1
40
dl
Since the line charge is lying on the y-axis, and taking into account the retarded potential, we can
further write the above as:
ky cos[ (t /c)]dy
1
V (r, t) =
40
where = [x2 +
1
Solutions to Quiz 3
(a) From the boundary condition, the surface charge is given by f = 0 n E since the electric
eld Eout in the conductor is zero. At x = 0, n = x, and at x = d, n = x, and the electric eld
between the ribbons is normal to the surface E
1
Solutions to Quiz 1
(a) The wave propagates in +z direction. The electric eld vector has an inclination of 450 with
the x-axis. The wave is linearly polarized since the x and y components are in phase, so that the
angle between the electric eld and the
1
Solutions to Quiz 2
(a) From the law of reection and transmission, sin(I )/sin(T = n2 /n1 . In this case, n1 = 1, n2 =
)
1.414, sin(T ) = sin(300 ) = 0.5, so sin(I ) = 1.414 0.5 = 22 , leading to I = 450 . So the sun
observed by David is 450 from zenith