Question

A thick current carrying cable of radius $R$ carries current $I$ uniformly distributed across its cross-section. The variation of magnetic field $B\left(r\right)$ due to the cable with the distance $r$ from the axis of the cable is represented by

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

From Ampere's circuital law,

$B_{inside}=\frac{{\mu }_{0}I}{2\pi R^2}\times r$, if $r<R$

$\Rightarrow B_{inside}\propto r$

$B_{outside}=\frac{{\mu }_{0}I}{2\pi r}$, if $r\ge R$

$\Rightarrow B_{outside}\propto \frac{1}{r}$

Hence, the correct plot of magnetic field $B$ with distance $r$ from axis of cable is given as,


Hence, $\left(D\right)$ is the correct answer.