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))`
B. `2((tau)/(sqrt3Bi))^(1//2)`
C. `(2)/(sqrt3) ((tau)/(Bi))^(1//2)`
D. `(1)/(sqrt3) (tau)/(Bi)`

Answer

B

Explanation

The current flowing clockwise in the equilateral traingle has a magnetic field in the direction `hat(k)` So, the torque acting on it is `tau= BiNA sin theta= BiN A sin 90^(@)`
`rArr tau = Bi xx (sqrt3)/(4) l^(2)` (area of equilateral triangle `=(sqrt3)/(4) l^(2)`) (as it appears that N=1)
`rArr ((4 tau)/(sqrt3 Bi)) =l^(2) rArr l=2 ((tau)/(sqrt3 Bi))^(1//2)`