Question

A uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current carrying coil in the shape of -

$\left(i\right)$ an equilateral triangle of side $a$.

$\left(ii\right)$ a square of side $a$.

The magnetic dipole moments of the coils in each case respectively are -

$I$ is the current through the coils.

• A. $4I{a}^2$ and $3I{a}^2$
• B. $\sqrt{3}I{a}^2$ and $3I{a}^2$
• C. $3I{a}^2$ and $I{a}^2$
• D. $3I{a}^2$ and $4I{a}^2$

Answer 1

The correct option is B $\sqrt{3}I{a}^2$ and $3I{a}^2$

Magnetic dipole moment of the equilateral shaped coil,

$\mu =nIA=\frac{12a}{3a}\times I\times \frac{\sqrt{3}}{4}{a}^2=\sqrt{3}I{a}^2$

Similarly, magnetic moment of the square shaped coil,

$\mu =nIA=\frac{12a}{4a}\times I\times a^2=3I{a}^2$

Hence, option $\left(B\right)$ is the correct answer.