Question

Two coils $A$ and $B$ having the radii in the ratio $1:2$ carrying currents in the ratio $5:1$ and have the number of turns in the ratio $1:5.$ The ratio of magnetic inductions at their centers is

• A. $5:1$
• B. $1:5$
• C. $2:1$
• D. $1:2$

Answer 1

The correct option is C $2:1$

Given,
$r_1:r_2=1:2;i_1:i_2=5:1;n_1:n_2=1:5$

The magnetic field at the center of the loop having $n$ turns is,

$B=\frac{{\mu }_{0}ni}{2r}\Rightarrow B\propto \frac{ni}{r}$

$\Rightarrow \frac{B_1}{B_2}$= $\frac{n_1{i}_1}{n_2{i}_2}$ $\times$$\frac{r_2}{r_1}$

$=\left(\frac{1\times 5}{5\times 1}\right)\times \frac{2}{1}=\frac{2}{1}$

$\therefore B_1:B_2=2:1$

​​​​​​​ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.