Question

A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be

• A. 2n B
• B. n${}^2$ B
• C. n B
• D. 2 n${}^2$ B

Answer 1

The correct option is B n${}^2$ B

$B=\frac{{\mu }_{0}i}{2R},n\times \left(2\pi r^{\prime }\right)=2\pi R$
$\Rightarrow n{r}^{\prime }=R$ ..... (1)

$B^{\prime }=\frac{n.{\pi }_i}{2r^{\prime }}$ ......... (2)

From (1) and (2),

$B^{\prime }=\frac{n{\mu }_{0}i.n}{2R}=n^{2}B$