These are just exercises.
e1. Derive eq. (2.5). Perform the numerical integration to find the fraction
of the induced charge on the front half facing the fixed charge q. Use the
two parameters in Fig. 2.3.
e2. Show that the force is indeed given by eq. (2.9).
For Q=2q, at what y will the force becomes attractive.
e3. From eq. (2.15) calculate the dipole moment from the induced surface
charge and show that the result is identical to the dipole moment from the
two image chages.
e4. Eq. (2.20) cannot be integrated analytically. This exercise requires
write a program to do numerical integration. Note that the problem has
cyclindrical symmetry so the answer does not depend on the azimuthal angle.
Calculate the potential for x ranges from a to 10a and theta from 0 to pi.
Present your results in a surface plot or a contour plot.
Note: The equation numbers are the same as in the 2nd edition.
problems from Jackson, chapter 2
p2.23 (prob 2.13 in the second edition)