Question

A current is flowing through a thin cylindrical shell of radius R. If energy density in the medium, due to magnetic field, at a distance r from axis of the shell is equal to U then which of the following graphs is correct

• A. a
• B. b
• C. c
• D. d

Answer 1

The correct option is B b

When a current flows through cylindrical shell, then according to Ampere circuital law, magnetic induction inside it will be equal to zero. Hence energy density at $r<R$ is equal to zero.
Therefore, (a), (c) and (d) are wrong.
When $r>R$, $B=\frac{{\mu }_{0}i}{2\pi r}$.
Since $U=\frac{B^2}{2{\mu }_0}$, therefore, outside the shell, $U=\frac{{\mu }_0{i}^2}{8{\pi }^2{r}^2}$. It means, just outside the shell, $U=\frac{{\mu }_0{i}^2}{8{\pi }^2{R}^2}$ and when $r\to \infty ,U\to 0$.
Hence (b) is correct.