HW 12 Phys5406 S06 not graded
1)Light enters one face of an optical ber, as in the notes, and is to undergo total internal
reection in the ber so that it travels to the other end. For n=1.5 and n=1.33, what are
the largest incident angles that allow this.
HW 4 Phys5405 f05 due 9/22/05
1) JDJ 11-5
2) JDJ 11-6, Sketch or plot versus in y, t in y, and distance in ly, where = v/c in the
earth frame.
3) JDJ 11-7
4) JDJ 11-8 part a
1
HW 4 Phys5405 f06 due Sept. 21
1) pistols are placed at Z=0.2 m so that they can be red in the X direction. The barrel
of the pistols ends at X=0. A meter stick at X= , where < 1 m moves in the positive
Z diection with speed V0 = 0.9c. When the center of
HW 4 Phys5405 f07 due 10/4/2007
This assignment will illustrate the use of relativistic kinematics by looking at some of
the reactions and decays pertinent to my current research project. The goal is to measure
the branching ratio for + to decay into e+ r
HW 3 Phys5406 S03 due 2/19/03
1) In an innite sea of constant magnetization, M, a long cylindrical hole of radius R is
drilled. If the axis of the hole is perpendicular to M, nd the magnetic eld B both inside
and outside the hole.
2) A sphere of radius R
HW 4 Phys5406 S05 due 2/17/05
1) This problem indicates how a permanent magnet works. Spherical geometry is used for
simplicity. Given a sphere of radius a and constant magnetization, M. Find the magnetic
eld B and also H both inside and outside the spher
HW 4 Phys5406 S06 due 2/23/06
IAe will use the solution for the empty ox with @xDyA a t za to get the qreen9s
funtion GD for ll prolems with this geometryF
A o see the onnetion etween r 2GD @r; r A a [email protected] r A nd sine seriesD expnd the
one dimensionl delt f
HW 4 Phys5406 S10 due 2/25/10
1) Consider two innite area, conducting, parallel plates. The plates are separated by a
distance D. They are maintained at constant potentials, V and V by baterries. Suppose
there is an innite plane of constant surface charge
HW 5 Phys5405 f01 due Nov. 8, 2001
It was pointed out to me that the nal exam date Dec. 19 is a Wednesday. The problems
below will be good practise for test 2 on Tu. Nov.6.
1) Show E B and B 2 E 2 /c2 are Lorentz Invariants
2) JDJ 11-13
3) JDJ 11-14 part
HW5 Phys5405 f02 due 10/15/02
1) JDJ 11-6 (Why must the calculation be carried out in terms of the Earth observers
variables? You may use the results of JDJ 11-5)
2) JDJ 11-8 (The last term occurs because n = n( ) and the frequency in the moving liquid
fr
HW5 Phys5405 f03 due 10/16/02
1) JDJ 11-8 part a only (make liberal use of approximations since =
2) JDJ 11-13
3) JDJ 11-22
4) Show E B and B 2 E 2 /c2 are Lorentz invariants.
5) JDJ 11-14 part b.
1
v
c/n
< 1).
HW 5 Phys5405 f04 due Oct. 7, 2004
1) JDJ 11-21 do part a) and the rst and last decays of part b)
2) JDJ 11-23.
3) JDJ 1-6 Also for part (a) obtain the force on a point charge Q between the plates and at
rest with respect to the plates in the reference fr
HW4 Phys5405 f02 due 10/8/02
1) JDJ 11-4
2) In O two evenly, but not exactly matched runners stand at (x,y,z) = (0,0,0) and (0,D,0),
where D = 1 m. Starters with guns stand very close to each runner. The starter at y=0
res his gun at t = 0 and at t = T =
HW 4 Phys5405 f01 due Nov. 1
Please have another look at new homework 3. I previously forgot an important constant.
1) JDJ chapter 11 problem 19
2) JDJ chapter 11 problem 20
3) JDJ chapter 11 problem 22
4) JDJ chapter 11 problem 23
5) JDJ chapter 11 probl
HW3 Phys5405 F05 due 9/15/05
1) In the notes we saw that the electrostatic eld changes discontinuously as you pass
through a layer of charge, while the potential is continuous. JDJ uses up alot of space
showing that the potential changes discontinuously w
HW 1 Phys5406 S10 due 1/28/10
1) In class we calculated the B eld on the axis of a circular loop of radius R carrying
current I. Now everywhere on the axis there is no current, so that the eld is derivable from
a scalar potential, . Calculate applicable f
HW 3 Phys5405 f06 due Sept. 14
1) JDJ chapter 1 problem 6
2) JDJ chapter 1 problem 10
3) An innitely long right circular cylinder has its axis along the z axis. The cylinder has
radius R and throughout its volume has uniform charge density 0 . A hole of r
HW 2 Phys5405 f01 due Sept. 13
1a) In a region of space E = Eex . Prove that E does not depend on y or z in this region.
1b) If there is no charge in this region, prove that E doesnt depend on x.
2a) Charge is arranged on the surface of a sphere of radius
HW3 Phys5405 f07 due 9/20/07
2
h
1) Show that the Schrodinger Equation, 2m
2
= ih , is invariant under the Galillean
t
transform, provided the wave function in the O frame is renormalized by a phase, = ei ,
where = mv (z vt/2) and z is the direction of
HW 3 Phys5406 S02 due Feb. 21,02
1) A right circular cylinder of radius R and innite length has constant permeability . The
cylinder is placed in a constant magnetic eld B directed perpendicular to the cylinder axis.
Find the resulting B, at arbitary poin
HW 3 Phys5406 S03 due 2/10/03
1)Recall the solution for the potential, (r), inside a conducting box of sides (a,b,c) in the
(x,y,z) directions when all sides are grounded except for the side at z = c that is maintained
at constant potential V,
(r) =
16V
s
HW 3 Phys5406 S04 due 2/24/04
1) A solid conducting sphere of radius R is cut into hemispheres and then glued together
with a thin layer of insulating glue. The hemisphere at positive z has potential V1 and
that at negative z has potential V2 . Find the p
HW 3 Phys5406 S05 due 2/10/05
1)Use the solution found in class for the potential, (r), inside a conducting box of sides
(a,b,c) in the (x,y,z) directions when all sides are grounded except for the side at z = c that
is maintained at potential V(x,y). In
HW 3 Phys5406 S06 due 2/9/06
IA here ws disussion in lss outD
g2
a
ZI
I
H
@
HA
dz G r; r ;
@IA
removing the depene of g2 on oth z9 nd zF o see this do tht [email protected] nd [email protected] ou
n do @A without solving prt @A y notingD @ a <=>AD nd
a ln2 C H2 PH os@ HA;
@PA
HW 3 Phys5406 S07 due 2/8/07
1)JDJ 4-13
2)A uncharged, conducting sphere of mass M and radius R oats with 1/4 of its volume
submerged in a dielectric liquid of permitivity . When a total free charge Q is put on the
sphere it oats with 1/2 its volume subme
HW 3 Phys5406 S08 due 2/7/07
1)A uncharged, conducting sphere of mass M and radius R oats with 1/4 of its volume
submerged in a dielectric liquid of permitivity . When a total free charge Q is put on the
sphere it oats with 1/2 its volume submerged. Calcu