Question

A square current carrying loop made of thin wire and having a mass m=10g can rotate without friction with respect to the vertical axis OO_I , passing through the center of the loop at right angles to two opposite sides of the loop. The loop is placed in a uniform magnetic field with an induction B=10^-1T directed at right angles to the plane of the drawing. A current I=2A is flowing in the loop. Find the period of small oscillations that the loop performs about its position of stable equilibrium. 

Answer 1

Consider a loop PQRS placed in uniform magnetic field B in such a way that the normal to coil subtends an angle  to the direction of B when a current I flows through the loop clockwise.

The sides PQ and RS are perpendicular to the field and equal and opposite forces of magnitude I and B act upwards and downwards respectively. Equal and opposite forces act on sides QR and PS towards right and left of coil. The resultant force is zero but resultant torque is not zero. The forces on sides PQ and RS produce a torque due to a single turn which is given by