Physics 361
Final Exam
December 17, 2009
This exam contains six problems to be completed in two hours of work
(or less). Each problems is weighted 15 points in your total examination
score.
Advice: each problem admits a simple, compact solution. Dont wast
Physics 361
Midterm Exam
Thursday October 13, 2011
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Vector Fields (20 points)
Solution
Many solutions are possible here. You can notice that the elect
Physics 361
Midterm Exam
Tuesday October 9, 2012
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Charge, Fields and Potentials (20 points)
A thin lm centered at the origin with width d and normal o
Physics 361
Midterm Exam
Tuesday October 9, 2012
1. Charge, Fields and Potentials (20 points)
Solution
(a) V depends only on z. Thus Ez = V /z = Vo (2/d 24z 2 /d3 ) inside the slab.
Notice that this is directed along the negative z direction for small z b
Physics 361
Homework Problems
Due: Thursday, September 3
DJG Problems 1.3, 1.131 , 1.15, 1.162 , 1.26
1
Evaluate the gradients in Cartesian coordinates and again in Spherical Polar Coordinates.
2
Carry out the calculation in Cartesian coordinates and in S
Physics 361
Homework Problems
Due: Thursday, September 10
DJG Problems 1.27, 1.28, 1.29, 1.36, 1.49, 1.61(a), 1.62
H2.P1 Gaussian representation of (3) ()
r
As an alternative to Griths Eqn. 1.96 we proposed a Gaussian represention of the
delta function
(
Physics 361
Homework Problems
Due: Thursday, September 17
DJG 2.31 , 2.72 , 2.9, 2.11, 2.12
1
To verify the far eld behavior when z > L calculate the x and z components of
the electric eld to leading order in the small dimensionless ratio L/z.
2
Gauss Law
Physics 361
Midterm Exam Solution Key
Thursday, October 1, 2015
1. Exercises with vector elds (20 points)
(a) A simple solution is to permute the triple scalar product
V dA = ( ex ) er dA = (r ) ex dA = 0
r
e
r
(1)
so the integrand (and integral) is zer
Physics 361
Midterm Exam
Thursday, November 19, 2015
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Boundary value problem (20 points)
(a) The exterior potential is a sum of separable solutions to
Physics 361
Midterm Exam
Thursday, October 1, 2015
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Exercises with vector elds (20 points)
r
For the vector eld V = ex evaluate three integrals on t
Physics 361
Midterm Exam
Thursday, October 13, 2011
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Vector Fields (20 points)
A curl-free vector eld F has a divergence D(r) = F which depends on dis
Physics 361
Midterm Exam
Tuesday October 19, 2010
1. Electrostatic Energy (20 points)
Solution
(a) The eld is measured in N/C. Thus [A] = N/C-m.
(b) There is a discontinuity Er = A(a b) at the surface of the sphere. Thus
a = o A(b a). Note that it is nega
Name:_
Physics 361
Prof. Williams
Midterm 2 Exam
November 12, 2013
1. Electric forces Near conducting Boundaries (20 points)
A grounded conducting sphere has an inner radius R 1 and outer radius R 2 as show. A charge q 1 is
embedded in the cavity, offset
Physics 361
Final Exam
December 17, 2009
1. Solvation Energy for a Uniform Ball of Charge
Solution: The electric eld in the conducting solution is zero in equilibrium. Thus
in the equilibrium state a free charge Q is induced on the boundary to the charge
1. Charged Shell and Dielectric
A spherical conductor with charge Q and radius a is embedded in a spherical dielectric
with dielectric constant K; inner radius a and outer radius 3).
Figure 1: A uniformly charged shell with charge Q and radius a is embedd
Physics 361
Midterm Exam
Nov. 23, 2010
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Point Charge Exterior to Biased Conductor (20 points)
A point charge q is a distance a above a spherical condu
Physics 361
Midterm Exam
Nov. 23, 2010
1. Point Charge Exterior to Biased Conductor (20 points)
(a) By the method of images for a grounded sphere, there is an induced image charge
q = qR/a. One can solve the problem for the biased conductor by superposing
Name:_
Physics 361
Prof. Williams
Midterm 1 Exam
October 1, 2013
1. Cylindrical charge and Potential Distribution (20 points)
A cylinder with radius R (and length > R) has an interior electric potential
V
<
2
( s ) = As ( s < R )
where s is the perpendicu
Physics 361
Midterm Exam
Nov. 18-19, 2008
Write your solutions to the following three problems in a white book and
return your completed examination book to my oce, DRL 2N17a, by 1
PM on Wed. November 19.
This exam is partially open book: you are permitte
Physics 361
Midterm Exam
Tuesday October 19, 2010
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Electrostatic Energy (20 points)
A solid sphere with outer radius a is hollowed out to an inner rad
Physics 361
Midterm Exam
Thursday, November 19, 2015
You have 75 minutes to complete the exam. The exam consists of three
problems weighted 20 points each.
1. Boundary value problem (20 points)
An isolated hollow spherical shell with radius R and surface