Question

A uniform conduction wire of length $10g$ and resistance $R$ is wound up into four turns as a current carrying coil in the shape of equilateral triangle of side $a$. If current $I$ is flowing through the coil then the magnetic moment of the coil is

• A. $\frac{\sqrt{3}}{2}{a}^{2}I$
• B. $\frac{a^{2}I}{\sqrt{3}}$
• C. $\sqrt{3}{a}^{2}I$
• D. $\frac{2a^{2}I}{\sqrt{3}}$

Answer 1

Answer: (C)

$\sqrt{3}{a}^{2}I$

It is given that

Number of turns $n=4$

Length of the uniform conducting wire $l=10a$

Area of an equilateral triangle $A=\frac{\sqrt{3}}{4}{a}^2$ where a is the side of triangle

Magnetic moment

$M=nIA$

$M=4\times I\times \frac{\sqrt{3}}{4}{\left(10\right)}^2$

$M=\sqrt{3}{a}^{2}I$