Question

A current is flowing along the length of a long thin cylindrical shell. Identify the correct options about magnetic field at different locations.

• A. Magnetic field at all the points lying inside the shell is zero
• B. Magnetic field at any point outside the shell varies inversely with distance from the surface of the shell
• C. Magnetic field strength is maximum just outside the shell
• D. None of the above

Answer 1

Answer: (A), (B), (C)

The correct options are
A Magnetic field at all the points lying inside the shell is zero
B Magnetic field at any point outside the shell varies inversely with distance from the surface of the shell
C Magnetic field strength is maximum just outside the shell

Using Ampere's law on the amperian loop of radius r centered at the axis of the cylinder is:
$\oint \overrightarrow{B}.dl={\mu }_0{I}_c$

For inside point, r<R
$\oint \overrightarrow{B}.dl=0$

or $B_{(}inside)=0$

So, magnetic field at all the points lying inside the shell is zero.

For outside point, r>R
$\oint \overrightarrow{B}.dl=B.\left(2\pi R\right)$

or $B_{(}outside)={\mu }_{0}I/2\pi R$

So, magnetic field strength is maximum just outside the shell i.e. at $r=R$.