Question

Two circular coils are made of two identical wires of same length and carry same current. If the number of turns of the two coils are $4$ and $2$, then the ratio of magnetic induction at the centres will be :

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

Answer 1

The correct option is D $4:1$

$B\alpha \frac{n}{r}$

Now wires have same length

So, $n_{1}2\pi r_1=n_2\times 2\pi r_2$

$4r_1=2r_2$

$\frac{r_1}{r_2}=\frac{1}{2}$, $\frac{B_1}{B_2}=\frac{\frac{n_1}{r_1}}{\frac{n_2}{r_2}}$

$\frac{B_1}{B_2}=\frac{n_1{r}_2}{n_2{r}_1}$

$\frac{B_1}{B_2}=\frac{4\times 2}{2\times 1}$

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