A U-shaped permanent magnet is rigidly fixed to a horizontal tabletop so that its two…
PHYSICS · Multi-part · CBSE · Physics · Magnetism and Matter · Magnetism and Matter
Problem
A U-shaped permanent magnet is rigidly fixed to a horizontal tabletop so that its two parallel prongs are separated by a distance 2a. The left prong is a North pole and the right prong is a South pole. A light bar magnet of negligible size compared with a is suspended from a fine, non-magnetic thread so that it can translate freely in the horizontal plane and also rotate about a vertical axis through its center. The bar magnet is initially released from rest at a point on the line that joins the tips of the prongs, exactly halfway between them. At the moment of release the bar magnet’s own North pole points toward the North prong, making a 45∘ angle with the line joining the prongs.
Answer the following, using clear reasoning based on magnetic interactions between poles.
(a) For the instant just after release, state the direction of the magnetic force acting on each pole of the suspended bar magnet (toward the left prong, toward the right prong, or neither). Justify your answer by identifying the relevant pole–pole interactions.
(b) Determine whether the net force on the suspended magnet is zero or non-zero. If non-zero, indicate its direction. Explain how you arrived at your conclusion.
(c) Determine whether the net torque on the suspended magnet about its center is zero or non-zero. If non-zero, indicate the sense of rotation (clockwise or counter-clockwise as viewed from above). Explain your reasoning.
(d) After sufficient time has passed, the suspended magnet comes to static equilibrium. Sketch its final position and orientation relative to the U-shaped magnet, and provide a brief explanation for that equilibrium configuration.