Question

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

• A. $\frac{{\mu }_{0}I}{a\pi }$
• B. $\frac{\sqrt{2}{\mu }_{0}I}{a\pi }$
• C. $\frac{{\mu }_{0}I}{\sqrt{2}a\pi }$
• D. $\frac{2\sqrt{2}{\mu }_{0}I}{a\pi }$

Answer 1

Answer: (D)

$\frac{2\sqrt{2}{\mu }_{0}I}{a\pi }$

$B_{total}=4B_{side}$

The magnetic field at the centre of the coil due to each side is in the same direction and are equal to each other,

$\therefore B_{total}=4\frac{{\mu }_{0}I}{4\pi \left(\frac{a}{2}\right)}[\sin \frac{\pi }{4}+\sin \frac{\pi }{4}]$

$B_{total}=\frac{2\sqrt{2}{\mu }_{0}I}{a\pi }$