Physics 322 Homework 4-sol
Assigned: Wed. 9/28/16
Due: Wed. 10/5/16
1. A capcitor consists of two parallel plates of area A and separation d A. It is charged to potential V . By considering
the change in energy of the system as the separation is altered b
Physics 322 Homework 1 sol
Assigned: Wed. 9/7/16
Due: Wed. 9/14/16
1. Suppose ~A = ~ f where 2 f = 0. Show that
~ ( f ~A) 0.
ans
We have
~ ( f ~A) =
f ~ ~A + ~A ~ f
f 2 f + |~ f |2 0
=
2. Show that
~A (~B C)
~ = ~B(~A C)
~ C(
~ ~A ~B)
~=
by computing the
Note Title 11/7/2016
CD
Problem 6.? An innitelyr long circular cylinder carries a uniform magnetization
M parallel to its axis. Find the magnetic eld (due to M inside and outside the
cylinder.
ms. Ti
.5. \
35=Vx=o wawvt
There 'I$ A unilLOfm 5111ch ecu-MT
. HNHSO
Note Title \ 11/23/2016
cfw_D Problem 9.1? Analyze the eaae ef pelariaatien perpendicular tn the plane af in-
cidence (Le. electrie elds in the y direeen, in Fig. 9.15]. hnpeae the lJ~t:-I:Inda1'j,r
cenditlena [Eq. 9.1m, and ehtain the Freanel e
Note Title 11/9/2016
0 Problem 111 A square loop is cutout of a thick sheet of aluminum. It is then placed
so that the top portion is in a uniform magnetic eld B, and is allowed to fall under
gravity (Fig. 120. (In the diagram, shading indicates the eld r
Physics 322 Midterm 2
December 2, 2016
name:
Reminder:
1. Box your final answer.
2. Attempt all the problems.
1
1 (20 pt)
2 (30 pt)
3 (30 pt)
4 (20 pt)
total (100 pt)
2
1. Suppose you are given a magnetized cube of a single edge length b centered about th
Note Title 10/31/2016
6)
Problem 5.26
(a) By 1Is'hatesi'er means you can think of (short of looking it up), nd the vector
potential a distance 5 from an innite: straight wire carrying a current I. Check
thatV-A=and? xA=B.
(h) Find the magnetic potential i
Physics 322 Homework 5
Assigned: Wed. 10/5/16
Due: Wed. 10/12/16
Note: First midterm is 10/14/16. You may want to photocopy your hw5 solutions for your midterm studies.
1. Griffiths 3.30
ans
a) The dipole moment formula from lecture is
Z
~p
=
d 0~r0 (~r0
Note Title 11/16/2016
Problem 7.34 A fat wire, radius :61, carries a constant current I, uniformly dis-
tributed over its cross section. A narrow gap in the wire, of width as < a, forms
a parallel-plate capacitor, as shown in Fig. 7.45. Find the magneti
Note Title 10/25/2016
1. An electric dipole moment pi is located at the center of a spherical uniform dielectric shell with inner radius A,
outer radius B, and dielectric constant X. Find the potential everywhere.
There are 3 regions of the potential:
3
V
Physics 322 Homework 2
Assigned: Wed. 9/14/16
Due: Wed. 9/21/16
1. Let ~F1 = x2 z and ~F2 = xx + yy + zz.
a) Calculate the divergence and curl of ~F1 and ~F2 .
ans
First, divergences:
~ ~F1 = 0
~ ~F2 = 3
Curls:
~ ~F1 = 2xy
~ ~F2 = 0
b) Which ~Fi can be wr
Physics 322 Homework 3-sol
Assigned: Wed. 9/21/16
Due: Wed. 9/28/16
1. Griffiths 2.27 (exercise in integrating the charge density for the potential). Leave the expression for V in terms of
an integral of the form
Z L/2
dz0 f (z z0 ).
V (0, 0, z) =
20 L/2
Since the last US employment release and comments from Yellen suggesting a December hike
is likely, gold has struggled to maintain its downward momentum. Whilst we believe that the Fed
will increase rates in December and gold prices will move lower over t
Physics 322 Homework 12
Assigned: Tues. 12/6/16
Due: Wed. 12/14/16
1. Griffiths 9.25
2. Here we want to consider the effective speed at which energy is transported in a rectangular waveguide for a T Emn
mode considered in lecture 34. Assume m 1 and n 1.
a
Phypsics 322 Midterm 1
October 14, 2016
name:
Box your nal answer.
1 (25 pt)
2 (30 pt)
3 (25 pt)
4 (20 pt)
total (100 pt)
1
1.
A uniform line charge is placed on an innite straight wire (parallel to the x axis), a distance H above a grounded
conducting pl
Physics 322 Midterm 2
Nov 30, 2015
name:
Box your final answer.
1 (15 pt)
2 (50 pt)
3 (20 pt)
4 (15 pt)
total (100 pt)
1
~ = M z. Compute
1. (15 pt) An infinitely long cylinder of radius R whose axis is parallel to the z axis has a uniform magnetization M
Name >
PHYSICS 322 Hour Exam
March 2, 1994
Do all four problems; they are of equal weight. Before beginning any long calculations, state
briey the principles you intend to use.
559?
/100
so = 8.85 x 10"12 fared/meter
[e] = 1.6 x 1019 Coulomb
me; =
Today in Physics 217: separation of variables IV
Separation in cylindrical
coordinates
Example of the split
cylinder (solution
sketched at right)
More on orthogonality of
trig functions and
Fouriers trick
V = V0
V =0
E
18 October 2002
Physics 217, Fall 20
Physics 322 Exam 2
Name;
(A)
Answers given without full justification/proof will not be accepted. Show all work
1.
r,
x
SC
An superconducting sphere of radius a is placed in an
Find
asymptotically uniform magnetic field B = B0 k.
B for r > a and (scalar
Physics 322 Exam 2
Name;
(A)
Answers given without full justification/proof will not be accepted. Show all work
1.
An infinite permeable cylinder of radius a and permeability is placed in an asymptotically uniform magnetic field
B = B0 j. Find B for s < a
The motion of charges
The Lorentz force law has a few surprises for you. If we write out the force law for the simple case of a constant
magnetic field B = B0 k and no magnetic field, we obtain
mv y = qB0 vx
mv x = qB0 vy ,
Multiplying the first by vx and
UIUC Physics 435 EM Fields & Sources I
Fall Semester, 2007
Lecture Notes 8
Prof. Steven Errede
LECTURE NOTES 8
POTENTIAL APPROXIMATION TECHNIQUES:
THE ELECTRIC MULTIPOLE EXPANSION
AND MOMENTS OF THE ELECTRIC CHARGE DISTRIBUTION
There are often situations
PHY311, Homework #1, DUE: Feb 5
Problem-1 Consider a functional of the form
Z x1
F (x, y, y 0 )dx,
v[y(x)] =
x0
1
F = ex (y 0 )2 2 y 2 .
2
(1)
Here and are some fixed constant parameters, which are independent of x and y. For this
functional derive corres
Physics 322 Final Exam
Dec, 2015
name:
Box your final answer.
1 (20 pt)
2 (30 pt)
3 (40 pt)
4 (20 pt)
5 (55 pt)
6 (20 pt)
7 (15 pt)
total (200 pt)
1
1. Maxwell equations in vacuum can be written in terms of scalar and vector potentials if we define
~B = ~