Question

A wire of length $l$ is bent into a circular coil of one turn of radius $R_1$ . Another wire of the same material and same area of cross section and same length is bent into a circular coil of two turns of radius $R_2$ . When the same current flows through the two coils, the ratio of magnetic induction at the centres of the two coils is :

• A. $1:2$
• B. $1:1$
• C. $1:4$
• D. $3:1$

Answer 1

The correct option is C $1:4$

Ist case:

$R_1=\frac{l}{2\pi }$, $n_1=1$

$\therefore B_1=\frac{n_1{\mu }_{0}i}{2R}$

=$\frac{1\times {\mu }_0}{\frac{2l}{1\pi }}$

=$\frac{1\times {\mu }_{0}i\pi }{l}$

IInd case:

$R_1=\frac{l}{4\pi }$, $n=2$

$B_2=\frac{2{\mu }_0.i}{2.\frac{l}{4\pi }}$

=$\frac{4\times {\mu }_0\pi }{l}$

$\frac{B_1}{B_2}=1:4$