Question

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns, find the magnetic field at the centre of this coil.

Answer 1

Initially, magnetic field at the centre of the circular loop, $B_0=\frac{{\mu }_{0}I}{2R}$
When $n$ turns are made of the wire, $2\pi R=n\times 2\pi R^{\prime }\Rightarrow R^{\prime }=\frac{R}{n}$
So, $B^{\prime }=\frac{{\mu }_{0}I}{2\left(\frac{R}{n}\right)}=n\frac{{\mu }_{0}I}{2R}$
$\therefore B^{\prime }=n{B}_0$