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)/(B.i))^(1//2)`
B. `2((tau)/(sqrt3B.i))`
C. `(2)/(sqrt3)((tau)/(B.i))`
D. `(1)/(sqrt3)(tau)/(B.i)`

Answer

b

Explanation

(b) `tau=MB sin theta`
`tau =iAB sin 90^(@)`
`therefore A=(tau)/(ib)`
Also, A=`1//2(BC)(AD)`
But `(1)/(2) (BC)(AD)=(1)/(2) (l) sqrt(l^(2)-((l)/(2^(2)))= (sqrt3)/(4)l^(2))`
`rArr (sqrt3)/(4)(l)^(2)=(tau)/(Bi) therefore l=2((tau)/(sqrt3i))^(1//2)`