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?
torque = IA x B = I(pi)r^2 x B
torque = r x F = r x (ma) = r x (m(r*alpha))
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