A coil in the shape of an equilateral triangle of side `l` is suspended between the pole pieces of permanent magnet. Such that `vecB` is in plane of the coil. If due to a current I in the triangle, a torque `tau` acts on it, the side l of the triangel is:

Options

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

Answer

a

Explanation

Torque acting on equilateral triangle in a magnetic field B is `tau=iABsintheta`

Area of triangle LMN,
`A=(sqrt(3))/(2)l^(2)andtheta=90^(@)`
Substituting the given values in expression for torque, we
get
`tau=ixx(sqrt(3))/(4)l^(2)Bsin90^(@)`
`tau-(sqrt(3))/(4)il^(2)B " " (becausesin90^(@)=1)`
Here , `l=2((tau)/(sqrt(3)Bi))^((1)/(2))`