Torque on a current carrying coil with an applied frictional force?

[discofmj]

Homework Statement

There's a diagram in my book but imagine a coil in a square shape attached to a vertical shaft, the diagram for convenience sake represents the coil as one circular wire exactly like a wire actually looks. However, the coil has 410 turns and has an area per turn of 3.1 X 10^-3 m². The magnetic field is 0.23 T, and the current in the coil is 0.26 A. A brake shoe is pressed perpendicularly against the shaft to keep the coil from turning. The coefficient of static friction between the shaft and the brake shoe is 0.76. The radius of the shaft is 0.012 m. What is the magnitude of the minimum normal force that the brake shoe exerts on the shaft?

Homework Equations

Torque = NIABsin(θ), f = u_sFn, Torque = Fd

The Attempt at a Solution

Because the coil does not rotate I assumed the force due to the torque on the coil acted oppositely to the force of friction which were the only two forces and they were equal to 0.
NIAB = u_sFn. I thought that since the equation is for torque that result needed to be divided by the perpendicular distance from the axis to the force, to give the force which when divided by the coefficient of friction would give the magnitude of the normal force. Can anyone help me?

 

[member 553083]

NIAB = 0.76FndFn = (NIAB)/(0.76d) Fn = (410 * 0.26 * 0.23 * 3.1 x 10^-3)/(0.76 * 0.012) Fn = 0.039 N