Question

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

• A. $2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$
• B. $\frac{2}{\sqrt3}(\frac{τ}{Bi})$
• C. $\frac{1}{\sqrt3}(\frac{τ}{Bi})$
• D. $\frac{2}{\sqrt3}(\frac{τ}{Bi})^{\frac{1}{2}}$

Answer 1

Answer: (A)

$2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$

Answer 2

The Correct option is A: $2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$

The current flowing clockwise in the equilateral triangle has a magnetic field in the direction of $\hat{k}$

τ = $BiNAsinθ$
τ = $BiNAsin90^o$

Area of equilateral triangle: $\frac{\sqrt{3}}4 I^2$

τ = $Bi×\frac{\sqrt{3}}4 I^2$

$\therefore I^2 = \frac{4τ}{\sqrt{3} Bi}$ = $2(\frac{τ}{\sqrt3Bi})^{\frac{1}{2}}$