Question

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

Answer: (A)

$\sqrt{3}\frac{{\mu }_{0}I}{2R}$

$\overrightarrow{B}=\frac{{\mu }_{0}I}{2R}(\pm \hat{i})+\frac{{\mu }_{0}I}{2R}(\pm \hat{j})+\frac{{\mu }_{0}I}{2R}(\pm \hat{k})$
$\left|\overrightarrow{B}\right|=\frac{{\mu }_{0}I}{2R}\sqrt{3}$