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 $\vec{B}$ 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 triangle is

• A. $\frac{2}{\sqrt 3} \bigg(\frac{\tau}{Bi} \bigg)$
• B. $2 \bigg(\frac{\tau}{\sqrt 3 Bi} \bigg)^{1/2}$
• C. $\frac{2}{\sqrt 3} \bigg(\frac{\tau}{Bi} \bigg)^{1/2}$
• D. $\frac{2}{\sqrt 3} \frac{\tau}{Bi}$

Answer 1

Answer: (B)

$2 \bigg(\frac{\tau}{\sqrt 3 Bi} \bigg)^{1/2}$

Answer 2

The current flowing clockwise in the equilateral triangle has a magnetic field in the direction $\widehat{k}$
$\tau = BiNAsin \theta = B\, iAsin90^\circ$
$\tau =$ $Bi\times\frac{\sqrt{3}}{4}l^{2}$ (area of equilateral triangle
$=\frac{\sqrt 3}{4} l^2)$
(as it appears that N = 1)
$\bigg(\frac{4\tau}{\sqrt 3 Bi} \bigg) = l^2 \Rightarrow l = 2\bigg(\frac{\tau}{ Bi \sqrt 3} \bigg)^{1/2}$.