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## Homework Statement

A wire loop, of mass "m" and radius "r"; in the x-y plane with a current "I" flowing through it in the clockwise direction is in a magnetic field. The field "B" is pointing along the x-axis. The magnetic field will exert a torque on the wire, causing the loop to rotate with a frequency "f".

What is the magnitude of the magnetic field?

## Homework Equations

torque = IA x B = I(pi)r^2 x B

torque = r x F = r x (ma) = r x (m(r*alpha))

theta(final)=theta(initial)+omega(initial)*t+(1/2)(alpha)t^2

## The Attempt at a Solution

Assuming that the initial angular velocity is zero.

A full revolution -> theta(final)=2*pi

time for a full revolution (period) -> T=1/f

angular acceleration -> alpha = 2*(2*pi)/T^2

torque = rF = r(ma) = r*m(r*alpha) = r^2*m*(4*pi/T^2)

torque = I*A*B = I*pi*r^2*B

r^2*m*4*pi/T^2 = I*pi*r^2*B

B = 4*m/I*T^2