Question

A long straight wire with a circular cross-section having radius $R$, is carrying a steady current $I$. The current $I$ is uniformly distributed across this cross-section. Then the variation of magnetic field due to current $I$ with distance $(r<R)$ from its centre will be

Answer 1

Current through the loop of radius $r$($r<R$) will not be $I$.

Using Ampere's Law, we can write;

$\int \overrightarrow{B}\cdot \overrightarrow{dl}={\mu }_0{I}_{In}$
$\Rightarrow B\times 2\pi r=\frac{{\mu }_{0}I}{\pi R^2}\times \pi r^2$
$\Rightarrow B\propto r$

$\Rightarrow$ Option $B$ is correct