Equations for Currents, Loops, and Torques

What equations are needed to solve this problem? How would the equations change if it was a circular loop?

a) A square loop of the side length (a) carries a current (i) in the clockwise direction. The loop is placed in a magnetic field at an angle of 45 degrees to it (you can rotate the loop about the field as you like to make the problem simpler). What are the forces and torques on the loop and what are the final position and velocity of the loop?

b) This loop is put on top of a second identical loop, so that they are concentric. The current in the first loop is clockwise and increasing - What will be the sign of the current in the second loop?

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Solution Preview

... F = BIL sinx ............. ( x = 90 is angle between B and QR )
= BIa ..............( L = a and sin90 = 1 )

The force on SP, F' is BILsin90 = BIa in the direction perpendicular to both SP and B at an angle of 45 degree with the vertical.

F and F' are equal, ...