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

Answer

C

Explanation

Torque acting on equilateral triangle in a magnetic field `vec(B)` is

`tau=iAB sin theta`
Area of triangle LMN
`A=sqrt(3)/4l^(2) and theta=90^(@)`
Substituting the given values in the expression for torque, we have
`tau=ixxsqrt(3)/4l^(2) B sin 90^(@)`
`=sqrt(3)/4il^(2)B , ( :' sin 90^(@)=1)`
Hence, `l=2(tau/(sqrt(3) Bi))^(1//2)`