You wind a square coil 0.150 m on a side from a 5.00-m long piece of wire that h

Question

You wind a square coil 0.150 m on a side from a 5.00-m long piece of wire that has a mass of 0.150 kg. You then suspend the coil from one side (with a hinge arrangement) in a 0.0400 T magnetic field directed vertically upward by running a current of 3.30 A through the coil as shown.

(a) When the coil is in rotational equilibrium, determine the angle that the plane of the coil makes with the vertical.

You wind a square coil 0.150 m on a side from a 5.00-m long piece of wire that has a mass of 0.150 kg. You then suspend the coil from one side (with a hinge arrangement) in a 0.0400 T magnetic field directed vertically upward by running a current of 3.30 A through the coil as shown.

Explanation / Answer

DIdn't work for me.

You dont want to find if the forces cancel. Find what angle makes the moment 0.

(.625)mg sin(theta)= (1.25)BIL cos(theta)

Also remember that the Forces for the the sides connected to the hinge cancel. and the force on the current on the hinge will just be canceled by the hinge's reaction force. So the only length we care about is the the one section L=5/4= 1.25m

sin(theta)/cos(theta) = 2BIL/mg

tan(theta) = 2BIL/mg

theta= arctan (2BIL/mg)

At least that is what worked for me for the first part.

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