Question

A circular disk rotates about its axis with angular velocity w. The disk is made of metal with conductivity g and thickness t.The rotating disk os pa;lced the pole faces of a magnet which produces a uniform magnetic field B over a small square area of size a² at the average distance r from the axis where B is perpendicular to the disk, Show that the approximate torque on the disk is B²a²r²wgt/2.

Answer 1

first of all the formula to show is incorrect dimensionally it should be B²a²r²wg /2t

solution: Resistance = length / conductivity * area

torque in a magnetic field = current * area *Magnetic field Sin (theta).......

now current I= emf produced / resistance = emf * conductivity * area/ length

so torque = emf produced * conductivity * area² * magnetic field * Sin 90⁰/length.........(2)

now emf produced in rotating disc of radius "r" in magnetic field "B" with angular velocity "w" is:

1/2 * B * r² * w (proof can be found eaisly) using this in equation (2)

torque =(1/2 )* B * r² * w * g * a² * B / t

torque = B²r²a²wg / 2*t