Question

Two concentric circular loops of radii $0.08m$ and $0.1m$ carry currents such that magnetic field at the centre is zero. If the current in the outer loop is $8A$ clockwise, current in the inner loop is

• A. 6.4 A anti-clockwise
• B. 6.4 A clockwise
• C. 8 A anti-clockwise
• D. 3.2 A clockwise

Answer 1

Answer: (A)

Here, $R_1=0.1m,R_2=0.08m,I_1=8A$
Magnetic field at centre $O$ due to current in outer loop, ${\vec{B}}_1=\frac{{\mu }_0{I}_1}{2R_1}\otimes$
Let the current in inner loop be $I_2$ and magnetic field at centre $O$ due to it be ${\vec{B}}_2$
As ${\vec{B}}_1+{\vec{B}}_2$ or ${\vec{B}}_1=-{\vec{B}}_2$
$\therefore I_2$ must be anti-clockwise and $|{\vec{B}}_1|=|{\vec{B}}_2|$
or, $\frac{{\mu }_0{I}_1}{2R_1}=\frac{u_0{I}_2}{2R_2}$
$\Rightarrow I_2=\frac{I_1}{R_1}\times R_2=\frac{8}{0.1}\times 0.08$
$=6.4A$