Physics 272: Advanced Honors Physics II
Spring 2018

Practice Exam 1 comments

Fall 2002 Exam
1. (b) The problem statement should have added "for charges Q and -Q on the two spheres."
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 (b).

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 systems.
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 desired point.

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.