Question

Let I₁ and I₂ be the steady currents passing through a long horizontal wire XY and PQ respectively. The wire PQ is fixed in horizontal plane and the wire XY be is allowed to move freely in a vertical plane. Let the wire XY is in equilibrium at a height d over the parallel wire PQ as shown in figure.

Answer 1

If the wire XY is slightly displaced and released, it executes simple uarmonic motion due to force of repulsion produced between the current carrying wire.

Acceleration of the wire, a = -ω²y 

Time period of oscillation of the wire,

T = 2π\(\sqrt{\frac{d}{g}}\)