Question

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

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

Answer 1

Answer: (A)

$\vec{B}=B_x \hat{i}+B_y \hat{j}+B_z \hat{k}$
$ \Rightarrow B=\sqrt{B_x^2+B_y^2+B_z^2}$
Since $B_x=B_y=B_z$ so $B=\sqrt{3} B_0$
$B=\sqrt{3} \frac{\mu_0 I}{2 R}$