An electric dipole
_{},
pointing in the *y* direction, is placed midway between two large
conducting plates, as shown in Figure 1. Each plate makes a small angle
*θ* with respect to the *x* axis, and they are maintained at
potentials ±*V*. What is the direction of the net force on
_{}?
Explain!

A point charge *q* is embedded at the center of a sphere of linear
dielectric material (with susceptibility *χ*_{e} and radius
*R*).

a) Find the electric field, the polarization and the bound charge.

b) What is the total bound charge on the surface?

c) Where is the compensating negative bound charge located?

a) Find the electric field, the polarization and the bound charge.

b) What is the total bound charge on the surface?

c) Where is the compensating negative bound charge located?

At the interface between one linear dielectric and another linear
dielectric the electric field lines bend (see Figure 2). Show that
tan*θ*_{2}/tan*θ*_{1} =
*ε*_{2}/*ε*_{1}, assuming that there is no
*free* charge at the boundary.

a) Find the force on a square loop placed as shown in Figure 3a, near an
infinite straight wire. Both the loop and the wire carry a steady current
*I*.

b) Find the force on a triangular loop placed as shown in Figure 3b, near an infinite straight wire. Both the loop and the wire carry a steady current*I*.

b) Find the force on a triangular loop placed as shown in Figure 3b, near an infinite straight wire. Both the loop and the wire carry a steady current

Suppose the magnetic field in some region has the form

where *k* is some constant. Find the force on a square loop of side
*s*, lying in the *yz* plane, centered at the origin, which carries a
current *I*.