Question

A wire of length $L$ carrying a current $I$ is bent into a circle. The magnitude of the magnetic field at the centre of the circle is

• A. $\frac{\pi \mu _{0} I}{L}$
• B. $\frac{\mu _{0} I}{2 L}$
• C. $\frac{2 \pi \mu_{0} I}{L}$
• D. $\frac{\mu _{0} I}{2 \pi L}$

Answer 1

Answer: (A)

Length $L=$ circumference of circle $=2\pi R$
$\Rightarrow R=\frac{L}{2 \pi }$
$\therefore \, $ Magnetic field at the centre of circular current loop is
$B=\frac{\mu _{0} I}{2 R}=\frac{\mu _{0} I}{2 \, L}\times 2\pi $
$B=\frac{\mu _{0} \pi I}{L}$