Question

A rectangular coil, with corners labeled ABCD, of Length L and width w is placed in a magnetic field B . If there is no current flowing through the coil, what is the force acting on Section AB of the coil.

is it ILB cos(theta)

Answer 1

Using the Lorentz Force Law, the force acting on each section of the coil is
$$
\mathbf{F} = I \boldsymbol{\ell} \times \mathbf{B} \,\!
$$
If there is no current flowing through the coil, then F=0.
http://en.wikipedia.org/wiki/Lorentz_force#Force_on_a_current-carrying_wire

Make sense?