Q. In the following figure a wire bent in the form of a regular polygon of $n$ sides is inscribed in a circle of radius $a$. Net magnetic field at centre will be
A) $\frac{\mu_{0}i}{2\pi a}\tan\frac{\pi}{n}$
B) $\frac{\mu_{0}ni}{2\pi a}\tan\frac{\pi}{n}$
C) $\frac{2}{\pi}\frac{ni}{a}\mu_{0}\tan\frac{\pi}{n}$
D) $\frac{ni}{2a}\mu_{0}\tan\frac{\pi}{n}$
Explanation
(b) Magnetic field at the centre due to one side
$B_{1} = \frac{\mu_{0}}{4\pi}.\frac{2i\sin\theta}{r},$ where $r = a\cos\theta$
So $B_{1} = \frac{\mu_{0}}{4\pi}.\frac{2i\sin\theta}{a\cos\theta} = \frac{\mu_{0}i}{2\pi a}\tan\theta$
Hence net magnetic field
$B_{net} = n \times \frac{\mu_{0}i}{2\pi a}\tan\frac{\pi}{n}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.