Question

A current I flows in the anticlockwise direction through a square loop of side a lying in the xoy plane with its center at the origin. The magnetic induction at the center of the square loop is

• A. $\frac{2\sqrt{2}{\mu }_{0}I}{\pi a}{\hat{e}}_x$
• B. $\frac{2\sqrt{2}{\mu }_{0}I}{\pi a}{\hat{e}}_z$
• C. $\frac{2\sqrt{2}{\mu }_{0}I}{\pi a^2}{\hat{e}}_z$
• D. $\frac{2\sqrt{2}{\mu }_{0}I}{\pi a^2}{\hat{e}}_x$

Answer 1

The correct option is B $\frac{2\sqrt{2}{\mu }_{0}I}{\pi a}{\hat{e}}_z$

Field due to one side of loop at O
$=4.\frac{\mu I}{4\pi \left(\frac{a}{2}\right)}\left(2\sin {45}^0\right)$
Field at O due to all four sides is along unit vector $\overline{e_z}$
$\therefore$ Total field
$=4.\frac{\mu I}{4\pi \left(\frac{a}{2}\right)}\left(2\sin {45}^0\right)=\frac{2\sqrt{2}{\mu }_{0}I}{\pi a}$