Question

Two concentric rings are kept in the same plane. Number of turns in each rings is $25$. Their radii are $50cm$ and $200cm$ and they carry electric currents of $0.1A$ and $0.2A$ respectively, in mutually opposite directions. The magnitude of the magnetic field produced at their centre is ____________ $T$.

• A. $2{\mu }_0$
• B. $4{\mu }_0$
• C. $\frac{10}{4}{\mu }_0$
• D. $\frac{5}{4}{\mu }_0$

Answer 1

Answer: (D)

$\frac{5}{4}{\mu }_0$

Given, $N_1=N_2=25$ turns
$R_1=50cm=0.5m$
$R_2=200cm=2m$
$i_1=0.1A,i_2=0.2A$
The magnitude of the magnetic field
$\Delta B=B_1-B_2$
$=\frac{{\mu }_0{N}_1{i}_1}{2R_1}-\frac{{\mu }_0{N}_2{i}_2}{2R_2}$
$=\frac{{\mu }_0\times 25}{2}(\frac{i_1}{R_1}-\frac{i_2}{R_2})$
$=\frac{{\mu }_0\times 25}{2}(\frac{0.1}{0.5}-\frac{0.2}{2})$
$=\frac{25}{2}{\mu }_0(\frac{1}{5}-\frac{1}{10})$
$=\frac{25}{2}{\mu }_0\left(\frac{2-1}{10}\right)$
$=\frac{25}{2}{\mu }_0\times \frac{1}{10}=\frac{25}{20}{\mu }_0=\frac{5}{4}{\mu }_0$