Physics 272: Advanced Honors Physics II
Exam 1 comments
Fall 2002 Exam
1. (b) The
problem statement should have added
"for charges Q and -Q on the two
Note also this is to be done
approximately. You are guided on how
to do this, so just follow the
instructions. You are told that the
charge distribution on each sphere is
uniform (that is approximately true
when d>>a). Then you can find an
exact expression for the potential
everywhere. Take the difference
between the potential for a point on
sphere 1 and a point on sphere 2.
Approximate the distance between the
center of one sphere and any point on
the other sphere as d to get the
leading order term for a << d.
(d) Use the capacitance found in part
2. Read carefully and make a diagram
so that you are not confused about
what r is.
(b) Remember we did this in class by
finding the potential energy of the
charge +Q in the presence of the
conducting plane. Make sure you
understand why you divide the
potential energy of the charge + image
charge configuration by 2. You can
also do this by finding the force on Q
as a function of h (it's just the
force from the image charge) and
integrating the work done when the
charge moves from h to infinity.
3. This is a very good problem that
tests your mastery of charge and
potential for spherically symmetric
For (b), just use the shell theorem.
For (c), you can use the shell theorem
for the field. For the potential, you
have to be more careful! Starting from
a, integrate inward to get to the
4. First compute dF on an
infinitesimal segment dx'' of wire 2
due to wire 1 (set up and evaluate the
integral). Then integrate dF over wire
2 to get the force exerted by wire 1
on wire 2.
(b) This could get out of control
unless you are careful. Organize your
ln term into a sum of terms with the
form ln(1+x) where x is small and
expand the ln to SECOND order: ln(1+x)
= x - x^2/2 + ...
5. Remember that the force acting on a
surface charge is sigma vec Eav.