Torque on cylinder due to current in loop

[Rabbittt]

Homework Statement

The figure shows a cylinder of mass 3.38 kg, radius 5.20 cm and length 8.12 cm with 70 turns of wire wrapped around it lengthwise, so that the plane of the wire loop is parallel to the incline and contains the axis of the cylinder. What is the least current which while flowing through the loop will prevent the cylinder from rolling or sliding down the inclined plane in the presence of a vertical magnetic field of B = 0.34 T? The angle of inclination http://lon-capa.mines.edu/adm/jsMath/fonts/cmmi10/alpha/100/char12.png = 22.0 degrees. The plane of the windings is parallel to the inclined plane. You should assume that the wires are wound much tighter than the figure implies (ie, assume that the wire loop has the same dimensions as the cylinder).

Homework Equations

Torque= IABsin(theta)

The Attempt at a Solution

I know I need to find the current so the net torque equals zero. I am confident that the torque due to a current is IABsin(theta). However I can't figure out what the torque due to the cylinders weight or friction might be. Any help would be greatly appreciated.

 

[Simon Bridge]

Draw a free body diagram.