Question

Two similar circular loops of radius $R$, are lying concentrically with their planes at right angles to each other. The currents flowing in them are $I$ and $I\sqrt{3}$ respectively. The magnetic field at the centre of the coil is :

• A. $\frac{{\mu }_{0}I}{2R}$
• B. $\frac{{\mu }_{0}I}{R}$
• C. $\frac{4{\mu }_{0}I}{R}$
• D. $\frac{\sqrt{3}{\mu }_{0}I}{R}$

Answer 1

The correct option is B $\frac{{\mu }_{0}I}{R}$

The magnetic field at the center of the circular coil of radius $R$ carrying current $I$ is given by

$B=\frac{{\mu }_{0}I}{2R}$. . . . . . .(1)

The magnetic field at the center of the circular coil of radius $R$ carrying current $\sqrt{3}I$ is given by

$B^{\prime }=\frac{\sqrt{3}{\mu }_{0}I}{2R}=B\sqrt{3}$ (from equation 1)

The net magnetic field,

$B_n=\sqrt{B^2+3B^2}=2B$

$B_n=2.\frac{{\mu }_{0}I}{2R}=\frac{{\mu }_{0}I}{R}$

The correct option is B.