Question

Two wires A and B are if lengths 40 cm and 30 cm.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 induction 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

Answer: (A)

3 : 4

For wire $A$ length $=40cm$ it is bent into a circle$,$

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

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

For wire $B$ length $=30cm$ it is bent into an arc$,$

So$,$ $\theta r=30$

Magnetic induction at centre due to circular arc $=\frac{{\mu }_0{i}_2\theta }{4\pi r}$

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

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

$\Rightarrow \frac{i_1}{i_2}=\frac{3}{4}$

Hence,

option $\left(A\right)$ is correct answer.