Problem 1:

An infinite cylinder of radius R, with its symmetry axis oriented along the z-axis, is filled with uniform charge density r.  Determine the electric field E(r), where r is the perpendicular distance from the z-axis.

Problem 2:

Determine the charge distribution that will give rise to the potential V(r) = kq exp(-mr)/r, with m a positive constants.  Calculate the total charge in the distribution.

Problem 3:

Problem 3:

A conductor at potential V = 0 has the shape of an infinite plane with a hemispherical bulge of radius R.  A charge q is placed above the center of the bulge, a distance d from the plane (which means a distance d - R from the top of the bulge).  What is the electrostatic force on the charge?

Problem 4:

A vertical thin rod of length L carries a total charge Q uniformly distributed.  Calculate the electric field along its axis at a distance z above its top end.

Problem 5:

A particle of mass m and charge e is suspended on a string of length L.  At a distance d (d > L) under the point of suspension there is an infinite plane conductor.  Ignore gravity.  Compute the frequency of the pendulum if the amplitude is sufficiently small such that Hooke’s law is valid.  (Ignore radiation losses).

Problem 6:

n identical spherical droplets of water, each charged to the same potential V, merge to form a larger droplet.  What will be its potential?

Problem 7:

A flat, insulating disk of radius R lies in the xy plane and is centered at the origin.  It has uniform surface charge density s.
(a)  Find the electric potential on the axis of the disk.
(b)  Find the limiting behavior of the potential when z >> R, and z << R.