Question

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

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

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