Question

A square loop of side 'a' carries a current $I$.The magnetic field at the centre of the loop is

• A. $\frac{2{\mu }_{o}I\sqrt{2}}{\pi a}$
• B. $\frac{{\mu }_{o}I\sqrt{2}}{\pi a}$
• C. $\frac{4{\mu }_{o}I\sqrt{2}}{\pi a}$
• D. $\frac{{\mu }_{o}I}{\pi a}$

Answer 1

The correct option is A $\frac{2{\mu }_{o}I\sqrt{2}}{\pi a}$

$B_c=4[\frac{{\mu }_o}{4\pi }\frac{I}{a/2}(sin{45}^o+sin{45}^o)]$

$=\frac{2\sqrt{2}{\mu }_{o}I}{\pi a}$