Question

A wire of length $L$ meters carrying a current $I$ amperes is bent in the form of a circle. The magnitude of the magnetic moment is:

• A. $\frac{L^2{I}^2}{4\pi }$
• B. $\frac{LI}{4{\pi }^2}$
• C. $\frac{L^{2}I}{4\pi }$
• D. $\frac{LI}{4\pi }$

Answer 1

Answer: (C)

$\frac{L^{2}I}{4\pi }$

Let the radius of the circular loop be $R$

$\therefore$ $L=2\pi R$ $⟹R=\frac{L}{2\pi }$

Area of the circular loop $A=\pi R^2=\pi \times \frac{L^2}{4{\pi }^2}=\frac{L^2}{4\pi }$

$\therefore$ Magnetic moment $\mu =IA=\frac{L^{2}I}{4\pi }$