Question

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

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

Answer 1

The correct option is B $2:1$

$B=\frac{{\mu }_{0}in{r}^2}{2(r^2+x^2{)}^{3/2}}$
Two coils are identical i.e., $i$ and $r$ are same.
At centre, $B=\frac{{\mu }_{0}in}{2r}$
$\therefore B\alpha n$

$\therefore \frac{B_1}{B_2}=\frac{n_1}{N_2}=\frac{4}{2}=\frac{2}{1}$