Question

A wire of length l carries a steady current. It is bent first to form a circular plane loop of one turn. The magnetic field at the centre of the loop is B. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same is

• A. B
• B. B/4
• C. 4B
• D. B/2

Answer 1

The correct option is C 4B

$\begin{array}{c}2\pi R=L\\ \Rightarrow R=\frac{L}{2\pi }\\ B=\frac{\mu oi}{2R}=\frac{\mu oi}{2.\left[\frac{L}{2\pi }\right]}=\frac{\mu oi}{L}=\frac{\mu i\pi }{L}\\ {\left(2\pi r\right)}^2=L\\ r=\frac{L}{4\pi }\\ B^{\prime }=\frac{\mu oi}{2r}\times 2=\frac{\mu oi}{r}=\frac{\mu oi}{2}.4\pi =4B\end{array}$

$\therefore$ Option $C$ is correct.