Question

A circular coil of radius r having n turns carries a current $i$. The magnetic induction at the centre of the coil is $B$. Now the coil is unwound and rewound with half the original radius. If the magnetic induction at the centre of the coil is to be the same, the current that should be passed through the coil is :

• A. $2i$
• B. $i$
• C. $0.5i$
• D. $0.25i$

Answer 1

The correct option is D $0.25i$

As it is wound with half initial radius.
$n\left(2Ar\right)=n^1\left(2A\frac{r}{2}\right)$
$n^1=2n$
$B=\frac{{\mu }_{0}ni}{2r}$
For B to be same. Let current passing be $i_1$
$B=\frac{{\mu }_{0}ni}{2r}=\frac{{\mu }_0{2}^1{i}^1}{2\left(\frac{r}{2}\right)}$
$⟹i^1=\frac{i}{4}$