Question

Three rings, each having equal radius $R$, are placed mutually perpendicular to each other and each having its centre at the origin of co-ordinate system. If current $I$ is flowing through each ring then the magnitude of the magnetic field at the common centre is

• A. $\sqrt{3}\frac{{\mu }_{0}I}{2R}$
• B. zero
• C. $(\sqrt{2}-1)\frac{{\mu }_{0}I}{2R}$
• D. $(\sqrt{3}-\sqrt{2})\frac{{\mu }_{0}I}{2R}$

Answer 1

The correct option is A $\sqrt{3}\frac{{\mu }_{0}I}{2R}$

Magnetic field at centre of the ring $\frac{{\mu }_{0}I}{2R}$
As the three rings are mutually perpendicular, the magnetic field due to each one of them will be mutually perpendicular.
$B_{net}=\frac{{\mu }_{0}I}{2R}(\pm \hat{i}\pm \hat{j}\pm \hat{k})$
$\Rightarrow |B_{net}|=\frac{\sqrt{3}{\mu }_{0}I}{2R}$