A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that ⃗B is in the plane of the coil. If due to a current i in the triangle a torque τ acts on it, the side l of the triangle is

Question

Accepted Answer

(2) 2(τ/(√3 Bi))^1/2. Given: one triangular turn of side l carrying current i, with ⃗B lying in the plane of the coil. Idea: τ=iAB sin θ with θ the angle between the normal and ⃗B. If ⃗B is in the plane of the coil, the normal is perpendicular to it, so θ=90° and sin θ=1. Area of an equilateral triangle: A=(√3)/4l². So τ=i (√3)/4l² B. Rearranging: l²=(4τ)/(√3 Bi). Taking the root: l=2(τ/(√3 Bi))^1/2.

A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that ⃗B is in the plane of the coil. If due to a current i in the triangle a torque τ acts on it, the side l of the triangle is

Step-by-step solution

Why the other options are wrong