Download Sample Final/Honors Exam in Electrodynamics

Oberlin College Physics 411
Sample Final/Honors Exam in Electrodynamics
These are questions you might get on a final exam or an honors exam on electrodynamics.
1. Maxwell equations. (This problem was given on an Honors Exam at Oberlin in the 1990s.) Write
down the Maxwell equations. You may use any consistent set of units, you may use relativistic or nonrelativistic notation, you may write down the equations in media or in vacuum. After writing down the
equations, interpret what each one says.
2. Alfven’s theorem. (Set by examiner Michael Brown, a plasma physicist, on Oberlin Honors Exam,
2010.) Griffiths, fourth edition, problem 7.63.
3. Rock concert. The Grateful Dead claim that their sound system is so effective that the listener
hears sound of nearly the same volume whether close to or far from the loudspeakers. Under what general
conditions can this claim be reasonably accurate? Under what conditions is it sure to fail? (Clue: Despite
appearances, this is an electrostatics problem.)
4. Stationary charge near two conductors. (Oberlin Honors Exam, 2009.) Two very large conducting planes are situated perpendicular to each other, and then grounded. Charge +Q is situated a distance
L from each plane, as shown. What is the magnitude and direction of the force on the charge due to the
planes?
+Q
L
L
5. Moving charge near a conductor. (Examiner Allan Blaer set this problem on the Honors Exam
taken by Dan Styer in May 1977.) A point charge q moves with constant velocity ~v parallel to the plane
surface of a “semi-infinite” conductor. Assume v c.
a. Suppose the conductor has infinite conductivity. Find the electric and magnetic fields at all points on
the surface of the conductor. Also find the surface current distribution of the conductor.
b. Suppose the conductor has very high, but finite, conductivity σ. Making bold but clearly stated
approximations, estimate the “frictional drag” force exerted on the charge by the conductor. (You
√
may find it useful to recall that the skin depth is given approximately by δ = c/ 2πσω for that
Fourier component of a pulse that has frequency ω.)
(Do not agonize over this problem: I haven’t yet solved it. But do think about how you would approach
such a difficult problem if it were given to you. You can’t solve it completely, but what can you do?)