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

Options

A. `(2)/(sqrt3) ((tau)/(Bi))^(1/2)`
B. `(2)/(3) ((tau)/(Bi))`
C. `2((tau)/(sqrt3 Bi))^(1/2)`
D. `(1)/(sqrt3) ((tau)/(Bi))`

Answer

C

Explanation

`tau = mB sin theta = iAB sin 90^(@)`
`A = (sqrt3)/(4)""i^(2)`
`therefore tau = (sqrt3)/(4) ""l^(2) iB`
`therefore l = 2 (( r)/(sqrt3 Bi))^(1/2)`