The rectangular loop of wire shown in the figure has a mass of 0.18 g per centim

Question

The rectangular loop of wire shown in the figure has a mass of 0.18 g per centimeter of length and is pivoted about side ab on a frictionless axis. The current in the wire is 8.1 A in the direction shown.

Part A
Find the magnitude of the magnetic field parallel to the y-axis that will cause the loop to swing up until its plane makes an angle of 30.0 with the yz-plane.

image URL: http://session.masteringphysics.com/problemAsset/1261736/1/YF-27-75.jpg

I tried to find the torque in terms of B, and relate it to the total force caused my magnetic field and gravity. I got confused of which equations and lengths to use, so I would greatly appreciate detailed steps :)

Explanation / Answer

Consider the equilibrium position of loop making an angle of 30.

Now, The 2 torques acting are due to gravitational and magnetic field.

Force of gravity can be assumed to act at centre of loop.

Torque due to Fg = mg sin 30 * L/2 ; L = length of side of loop.

Torque due to B = X B [cross product]

= IAB sin60 ; I = current, A = area ; 60 = angle between area vector and B {Along y axis}

mg sin30 * L/2 = IAB sin60

B = 0.8 mT [g is taken to be 10]

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