Question

A thin, straight conductor lies along the axis of a hollow conductor of radius $R$ and both carry equal currents in the same direction. The magnetic field $B$ is plotted against the distance $r$ from the axis. Which of the following best represents the resulting curve ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C


As we know that magnetic field inside the hollow cylinder $(r\le R)$ will be due to long wire only.

$B_{inside}=\frac{{\mu }_{0}I}{2\pi r}.....\left(1\right)$

But outside the hollow cylinder $(r\ge R)$, magnetic field will be produce due to long wire as well as hollow cylinder.

$B_{outside}=B_{longwire}+B_{hollowcylinder}$

$B_{outside}=\frac{{\mu }_{0}I}{2\pi r}+\frac{{\mu }_{0}I}{2\pi r}$

$B_{outside}=\frac{{\mu }_{0}I}{\pi r}........\left(2\right)$

From eqautions $\left(1\right)$ and $\left(2\right)$, we can say that

$B\propto \frac{1}{r}$ and

$B_{\text{outside}}>B_{\text{inside}}\text{at}r=R$

Hence, option $\left(c\right)$ is correct.