Question

A coil in the shape of an equilateral triangle of side 0.02 m is suspended from the vertex such that it is hanging in a vertical plane between the role-pieces of a permanent magnet producing a horizontal magnetic field of $5\times {10}^{-2}T$. When a current of 0.1 A passed through it and the magnetic field is parallel to its plane through couple acting on the coil is:-

• A. $8.65\times {10}^{-7}N-m$
• B. $6.65\times {10}^{-7}N-m$
• C. $3.35\times {10}^{-7}N-m$
• D. $3.91\times {10}^{-7}N-m$

Answer 1

The correct option is A $8.65\times {10}^{-7}N-m$

Given,

Side of equilateral triangle, $a=0.02m$

Magnetic fiels, $B=5\times {10}^{-2}T$

Current passed through the coil, $I=0.1A$

As the coils is in the form of an eqiuilateral triangle, its area is,

$A=\frac{\sqrt{3}}{4}\times 0.02\times 0.02$

$A=\sqrt{3}\times {10}^{-4}m$

Torque on current carrying coil in magnetic field is,

$\tau =BINAsin\alpha$

where,

$\alpha ={90}^0$ and $N=1$

Then,

$\tau =BIA$

$5\times {10}^{-2}\times 0.1\times \sqrt{3}\times {10}^{-4}N-m$

$=8.65\times {10}^{-7}N-m$