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Physics 321: Electromagnetism I Name (Print):Spring 2014 ID:
Midterm 1 April 25, 2014, 12:30pmInstructor: Chris Laumann
Time Limit: 50 Minutes
Do not turn this page until the buzzers goes at 12:30.
Hand your exam to me before I leave the room at 1:25.
Please write your name on every page and your student ID on the
first page.
This exam contains 6 pages (including this cover page) and 6
problems.
This is a closed book exam. No books, notes or calculators
allowed.
Write all your work on these sheets. If you needmore space, you
may use the back of the frontpage; clearly indicate when you have
done this.
Organize your work, in a reasonably neat andcoherent way, in the
space provided. Work scat-tered all over the page without a clear
orderingwill receive very little credit.
Mysterious or unsupported answers willnot receive full credit. A
correct answer, un-
supported by calculations or explanations willreceive no credit;
an incorrect answer supportedby substantially correct calculations
and expla-nations will receive partial credit.
Problem Points Score
1 8
2 15
3 12
4 30
5 5
6 18
Total: 88
Mephistopheles: I must confess, my stepping oerThy threshold a
slight hindrance doth impede;The wizard-foot doth me retain.
Faust: The pentagram thy peace doth mar?To me, thou son of hell,
explain,How camest thou in, if this thine exit bar?Could such a
spirit aught ensnare?
MephistophelesObserve it well, it is not drawn with care,One of
the angles, that which points without,Is, as thou seest, not quite
closed.
Goethes Faust (1808)
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Midterm 1 - Page 2 of 6 Name:
Extra work page. Please indicate clearly which problem your work
isfor if you want it graded.
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Midterm 1 - Page 3 of 6 Name:
1. (8 points) Write carefully the pair of equations relating (r)
and V(r).
2. Suppose the electric field throughout a sphere of radiusR is
given by E(r) =ar r + bx.
(a) (8 points) What is the charge Q contained in the sphere?
(b) (7 points) Ifb were changed to 2b, how does the charge
density within the spherechange? How is this possible?
3. A cube of side length a centered on the origin contains a
charge density (r) =bz.
(a) (5 points) How much charge is in the cube?
(b) (7 points) What is electric field E(r)? Be as explicit as
you can about your method
and coordinates. You dont need to evaluate any definite
integrals but you need tosetup them up completely.
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Midterm 1 - Page 4 of 6 Name:
4. Faust wishes to summon Mephistopheles into his chamber from
the netherworld. Asdemons are by nature negative, Faust places 5
positive charges q at the points of apentagram (regular pentagon,
see below) on his floor (the x y plane) at a distance afrom the
origin, hoping to attract the beast. Assume one of the points is on
the y-axis.
(a) (5 points) Without a calculation, in what direction is the
electric field Eon the z
axis? What symmetry justifies your answer?
(b) (5 points) What is the potential V(z) on the z-axis?
(c) (5 points) What is the electric field E(z) on the
z-axis?
(d) (5 points) Sketch the field lines and equipotentials in the
x y plane. Label anyspecial lines in the plane where you know
exactly what direction the field points bysymmetry.
q
qq
q
q
x
y
a
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Midterm 1 - Page 5 of 6 Name:
(e) (5 points) Mephistopheles resides in the underworld directly
below Fausts chamberbut very far away atz= L. As physicists, you
may treat him as a spherical pointdemon with chargeQand massM. If
he begins at rest in the underworld, with whatvelocity does
Mephistopheles arrive in the center of Fausts pentagram? Assumethat
Mephistopheles flies freely subject only to the electrostatic
force.
(f) (5 points) Suppose Faust accidentally places the point on
the y-axis a little bitcloser to the origin than he intended.
Sketch what happens to Mephistophelestrajectory in the y zplane (no
calculation required).
5. (5 points) A pair of conductors carry chargeq1= Q and q2= Q
and potential V1 andV2 respectively. What is their mutual
capacitance?
q1, V1 q2, V2
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Midterm 1 - Page 6 of 6 Name:
6. A spherical capacitor consists of two concentric spherical
conducting shells of radiia andb (b > a) with vacuum in between
and outside them. There is +Q charge on the outersphere and Qon the
inner sphere.
(a) (5 points) Sketch on the figure where the potential is a
constant in space.
Q
-Q
(b) (5 points) Now, actually calculate the potentialV(r)
everywhere in space.
(c) (8 points) Calculate the stored potential energy using two
different approaches.
