We finished discussing the solution of electrostatic problems with the method of images. We discussed several examples, making the connection between the practical method of solution and the Green function that defines the general solution of the Poisson equation. A number of questions came up in a ``brainstorming'' fashion , about the solution of different problems, the role of the Green functions, the choices of boundary conditions and more ... This class has an excellent level of involvement and interactions. Let's keep on going this way!
We covered most of Ch.2 of Jackson.
4th Homework
1) A charge "Q" is located at a distance "d" from a conducting plane. Calculate the work done to move this charge from its position to an infinite distance from the plane.
2) An infinitely long wire runs parallel to the surface of a conducting plane
at a distance "h" from the plane. The wire carries a charge per unit
length "lambda".
a) What is the electric field at the surface?
b) What is the force per unit length acting on the wire?
3) A conducting spherical shell of radius "a" is charged with charge "Q".
Find the potential at an arbitrary point: i) inside the shell; ii) outside the
shell, by direct intergration.
Hint: Convince yourself that the field point can be chosen on the z-axis
without loss of generality.
4) Two concentric spherical conducting shells of radii r1 and r2 (r1 < r2) are kept at fixed potentials V1 and V2 respectively. Find the potential between the shells and at r>r2.