Question

Two concentric circular loops of radii $0.08\text{m}$ and $0.1\text{m}$ carries current such that magnetic field at the centre is zero. If the current in the outer loop is $8\text{A}$ clockwise, then the current in the inner loop is

• A. $6.4\text{A}$ anticlockwise
• B. $6.4\text{A}$ clockwise
• C. $8\text{A}$ anticlockwise
• D. $3.2\text{A}$ clockwise

Answer 1

The correct option is A $6.4\text{A}$ anticlockwise


Given:
$r=0.08\text{m};R=0.1\text{m};I_2=8\text{A}$

As the magnetic field at the centre is zero. So the magnetic field at the centre due to the outer loop must be cancelled by the inner loop. It means direction of current in both the loops must be opposite.

As the current in the outer loop is in clockwise direction, so current in the inner loop is anticlockwise.

Now we have decided the direction. Let's calculate the magnetic field.

As the net magnetic field is zero at centre,

${\overrightarrow{B}}_{\text{centre}}={\overrightarrow{B}}_{\text{inner}}+{\overrightarrow{B}}_{\text{outer}}=0$

${\overrightarrow{B}}_{\text{inner}}=-{\overrightarrow{B}}_{\text{outer}}$

$\left|{\overrightarrow{B}}_{\text{inner}}\right|=\left|{\overrightarrow{B}}_{\text{outer}}\right|$

applying the formula, $B=\frac{{\mu }_{0}I}{2a}$

$\frac{{\mu }_0{I}_{\text{inner}}}{2r}=\frac{{\mu }_0{I}_2}{2R}$

$\frac{{\mu }_0\times I_{\text{inner}}}{2\times \left(0.08\right)}=\frac{{\mu }_0\times 8}{2\times \left(0.1\right)}$

$I_{\text{inner}}=\frac{8\times 0.08}{0.1}=6.4\text{A}$

So answer is $6.4\text{A}$ (anticlockwise)