Question

Two wires A and B are of lengths 40cm and 30cm. A is bent into a circle of radius r and B into an arc of radius r. A current $i_1$ is passed through A and $i_2$ through B. To have the same magnetic inductions at the centre, the ratio of $i_1$:$i_2$ is :

• A. 3 : 4
• B. 3 : 5
• C. 2 : 3
• D. 4 : 3

Answer 1

The correct option is A 3 : 4

For wire $A$ , length $=40cm$

It is bent into a circle, so

$2\pi r=40r=\frac{40}{2\pi }$

Magnetic induction at center $=\frac{{\mu }_0}{2r}{.i}_1$

For wire $B$ length $=30cm$

It is bent into an arc so ${\theta }_r=30$

Magnetic induction at center due to circular arc

$=\frac{{\mu }_0}{4\pi r}{.i}_2\theta$

Since, $\frac{{\mu }_0}{2r}{.i}_1=\frac{{\mu }_0}{4\pi r}{.i}_2\theta$

$\frac{i_1}{i_2}=\frac{\theta }{2\pi }=\frac{30\times 2\pi }{2\pi \times 40}\frac{i_1}{i_2}=\frac{3}{4}$

Hence the correct answer is $\frac{3}{4}$