Question

A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius $R_1$ and the outer conductor is hollow of inner radius $R_2$ and outer radius $R_3$. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as

Answer 1

For : $r\le R_1,$

Magnetic field at an inside point of a cylinder given by

$B=\frac{{\mu }_{0}ir}{2\pi R^2}$
$\Rightarrow B\alpha r$

So, for $r\le R_1,B$ is linearly increasing.
So, option A and B are wrong.

For: $R_1\le r\le R_2,$
Between $R_{1}and{R}_2$ magnetic field due to outside cylinder will be zero.
Magnetic field due to inside cylinder will be
$B=\frac{{\mu }_{0}i}{2\pi r}$
$\Rightarrow B\alpha \frac{1}{r}$

So, graph is inverted hyperbola for
$R_1\le r\le R_2$

For : $R_2\le r\le R_3$
Magnetic field due to cylinder will be
$B=\frac{{\mu }_{0}i}{2\pi r}$

$\Rightarrow B\alpha \frac{1}{r}$

So, from the above conditions, the graph in option C is correct

Hence, correct option is (C).