Question

A long, straight wire of radius R carries a current distributed uniformly over its cross-section. The
magnitude of the magnetic field is

• A. maximum at the axis of the wire
• B. minimum at the axis of the wire
• C. maximum at the surface of the wire
• D. minimum at the surface of the wire.

Answer 1

Answer: (B), (C)

The correct options are
B minimum at the axis of the wire
C maximum at the surface of the wire

Current enclosed over circular cross section ares $\pi r^2$ is,

$I^{\prime }=I\left(\frac{\pi r^2}{\pi R^2}\right)$

$=I{\left(\frac{r}{R}\right)}^2$

Using Ampere law,

$\oint B\times dl=\frac{I_{enclosed}}{\mu }$

$B\times 2\pi r=\frac{I\left(\frac{\pi r^2}{\pi R^2}\right)}{\mu }$

$B=\frac{I}{\mu \left(2\pi R^2\right)}r$ ..(1)

$B$ is minimum at $r=0$ axis of the wire.

if $r>R$ then,

$B=\frac{I}{2\pi r}$ ..(2)

$B$ is maximum at $r=R$ at the surface of the wire.

where $I$=current flowing in wire.

so option B and C is correct.