Question

A given length of wire can be bent to form a circle or a square of single turn and a current may be established in it. The ratio of magnetic field at the centre of circle to that at the centre of square is :

• A. $\frac{{\pi }^2}{8\sqrt{2}}$
• B. $\frac{4\sqrt{2}}{{\pi }^2}$
• C. $\frac{\pi }{2\sqrt{2}}$
• D. $1$

Answer 1

The correct option is A $\frac{{\pi }^2}{8\sqrt{2}}$

Magnetic field of square =$B_s=\frac{2\sqrt{2}{\mu }_{0}I}{\pi L}$

Magnetic field of circle=$B_c=\frac{{\mu }_{0}I\pi }{4L}$

$⟹\frac{B_c}{B_s}=\frac{{\mu }_{0}I\pi }{4L}\times \frac{2\sqrt{2}{\mu }_{0}I}{\pi L}=\frac{{\pi }^2}{8\sqrt{2}}$