A uniform line charge *λ* is placed on an infinite straight
wire, a distance *d* above a grounded conducting plane. The wire runs
parallel to the *x* axis and directly above it, and the conducting plane is
the *xy* plane.

a) Find the potential in the region above the plane.

b) Find the charge density*σ* induced on the conducting
plane.

a) Find the potential in the region above the plane.

b) Find the charge density

In Example 3.2 of Griffiths we assumed that the conducting sphere was
grounded (*V* = 0). But with the addition of a second image charge, the
same model will handle the case of a sphere at *any* given potential
*V*_{0} (relative, of course, to zero at infinity).

a) What charge should you use, and where should you put it?

b) Find the force between a point charge*q* and a conducting sphere at potential
*V*_{0}.

a) What charge should you use, and where should you put it?

b) Find the force between a point charge

Two infinite parallel grounded conducting planes are held a distance
*a* apart. A point charge *q* is placed in the region between them, a
distance *x* from one plate.

a) Find the force on*q*.

b) Check that your answer is correct for the special case in which*a* →
∞. Check that your answer is correct for the special case in which
*x* = *a*/2.

a) Find the force on

b) Check that your answer is correct for the special case in which

A long rectangular pipe, running parallel to the *z* axis, has three
grounded metal sides, at *y* = 0, *y* = *π*, and *x* =
0. The fourth side, at *x* = *a*, is maintained at a specified
potential *V*_{0}(*y*).

a) Develop a general formula for the potential within the pipe.

b) Find the potential explicitly, for the case*V*_{0}(*y*) = *V*_{0} = constant.

a) Develop a general formula for the potential within the pipe.

b) Find the potential explicitly, for the case

A cubical box consists of five metal sides (length of each side is
*π*) which are welded together and grounded (see Figure 1). The top
is made of a separate sheet of metal, insulated from the rest, and held at a
constant potential *V*_{0} by a battery. Find the potential inside
the box.