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. The magnetic field at the centre of this coil of n turns will be
(1) nB
(2) n² B
(3) 2nB
(4) 2n² B

Answer 1

Explanation:

The circumference of the first loop is the length of the wire=2πR

The magnetic field at the center of this wire=B=2Rμ0I

The same wire is bent into n circular coils.

Thus new radius is found out by

n×2πr=2πR

⟹r=nR

Thus magnetic field at the center of these loops=n2rμ0I

=2Rn2μ0I=n2B