Question

A coil in the shape of an equilateral triangle of side $0.02\, m$ is suspended from its vertex such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a uniform field of $5 \times 10^{-2} T$. If a current of $0.1\, A$ is passed through the coil, what is the couple acting?

• A. $5 \sqrt 3 \times 10^{-7}N-m $
• B. $5 \sqrt 3 \times 10^{-10}N-m $
• C. $\frac {\sqrt 3}{5} \times 10^{-7} N-m $
• D. None of these

Answer 1

Answer: (A)

Torque $\tau=i A B \sin \theta, i=0.1 A, \theta=90^{\circ}$
$A=\frac{1}{2} \times$ base $\times$ height
or $A=\frac{1}{2} a \times \frac{a \sqrt{3}}{2}$
$=\frac{\sqrt{3} a^{2}}{4}=\frac{\sqrt{3} \times(0.02)^{2}}{4}$
$=\sqrt{3} \times 10^{-4} m^{2} ; \theta=90^{\circ}$
$\tau=0.1 \times \sqrt{3} \times 10^{-4} \times 5 \times 10^{-2} \sin 90^{\circ}$
$=5 \sqrt{3} \times 10^{-7} N-m$