Home Work Set # 6, Physics 217, Due: October 24,
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
b) Find the charge density σ induced on the conducting
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
V0 (relative, of course, to zero at infinity).
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
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.
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 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
a) Develop a general formula for
the potential within the pipe.
b) Find the potential explicitly, for the case
V0(y) = V0 = constant.
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 V0 by a battery. Find the potential inside
1. Problem 5.