Physics 435
Discussion 6
Solution
September 28, 2015
Exam review:
1. A slab of thickness 2d in the z-direction (!d z +d ) and
(
( )
d"
z"
2
infinite in x and y contains a charge density (z) = 0 1
.
!
= 0 everywhere outside the slab (i.e., for ! z > d ).
1. Discussion 1: Divergence Theorem
(1) Griffiths 1.33
+ 3zx
We will do the easier part first (i.e. integrate the divergence of v = xy
x + 2yz y
z over
the volume). We first need to compute v which is in Cartesian coordinates is just:
xy 2yz 3zx
+
+
x
y
Physics 435
Discussion 5
Solution
September 21, 2015
1. This is similar to the lecture example.
An infinitely long rectangular pipe runs parallel to the z-axis (from - to +). Three sides
are grounded (V = 0). The one at x = b is maintained at a specified
Physics 435
Discussion 4
Solution
September 14, 2015
1. Find the general solution to Laplaces equation in cylindrical coordinates, assuming that
1 V 1 2V
there is no z-dependence. That is, solve this equation: 2V ( s, ) =
=0.
s +
s s s s2 2
!
Comment: Bec
Physics 435
Discussion 3
Solution
September 7, 2015
1. Poissons equation is very important in many areas of physics. Schrdingers equation in
quantum mechanics is a version of this equation. So, it is very important to understand the
various forms its solu
Physics 435
Discussion 2
Solution
August 31, 2015
1. Consider an extension of the example on p. 14 of my lecture notes. Now, each of the objects
is described by its velocity, v , as well as its mass, charge and position. Write the possible
forms that the
Physics 435
Discussion 1
August 24, 2015
Math review.
1. The dot (inner) product.
a. Calculate the dot product of these two vectors: v1 = (1,3,5) , v2 = ( 2,4,6 ) . .
The dot product is: v1.v2 = v1xv2x + v1yv2y + v1zv2z = 12 + 34 + 56 = 44.
b. Calculate t
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Physics 435
Homework 4
Solution
Due September 21, 2015
1. A point charge, q, is placed inside a hollow, grounded spherical shell of radius
R, a distance a away from the center, as shown. There is no other charge
a q
besides q and what is needed on the sph
Du
eAp
r
i
l1
8
,
2
0
1
6
N!turns!of!wire!
2. An air-filled torus is wound with N turns of wire. It has inner
radius a and outer radius b and a circular cross section of
radius (b-a)/2.
a. Calculate its self-inductance.
a"
b"
I
Amperes law tells us that t
Physics 435
Due May 2, 2016
Homework 14
Solution
1. The current in a long solenoid (end view is shown) increases linearly with time, so the flux is
proportional to t: = t . Two ideal voltmeters (infinite resistance no current flows
through them) are conne
Physics 435
Due January 25, 2016
Homework 1
This is some math review.
Each problem is worth five points.
In this course, all HW problems will have the same value unless stated otherwise.
!
1. Calculate the line integral of the function v = 3zx + xzy + z 2
Physics 435
Homework 8
Solution
1. A grounded conducting sphere of radius R1 is wrapped in a
spherical shell of dielectric (r) of outer radius R2. It is placed
in an otherwise uniform external electric field, E0. Calculate
V(r,) everywhere.
Due October 19
Physics 435
Due February 8, 2016
Homework 3
Solution
NOTE: Problem 4 is worth 10 points.
1. Use Gausss law to find the electric field inside and outside an infinitely long wire of radius
S. The (volume) charge density in the wire is a function only of the
Physics 435
Homework 6
Solution
Due February 29, 2016
1. Remember Physics 214: The electrons in a metal are confined to a finite depth square well.
This means that they penetrate a short distance into the forbidden region outside the metal.
The positive c