Help with magnetic forces problem Is my solution correct?

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The discussion revolves around calculating the magnitude of the magnetic field affecting a wire loop with a current. The user derives the relationship between torque, angular acceleration, and the magnetic field using equations of motion and electromagnetic principles. They conclude that the magnetic field can be expressed as B = 4*m/I*T^2, assuming initial angular velocity is zero. The user seeks confirmation of this solution from others in the forum. The accuracy of the derived formula and the assumptions made are the main focus of the discussion.
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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
 
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