Question
If a long hollow copper pipe carries a current, then magnetic field is produced
A.
inside the pipe only
B.
outside the pipe only
C.
both inside and outside the pipe
D.
no where
Answer :
outside the pipe only
Solution :
According to Ampere’s circuital law,
$$\int {B \cdot dl = {\mu _0}{i_{{\text{enclosed}}}}} $$
So, $$B\left( {2\pi r} \right) = {\mu _0} \times 0\,\,\left[ {{i_{{\text{enclosed}}}} = 0} \right]$$
$$\therefore B = 0$$
So, inside a hollow metallic (copper) pipe there is no current inside the Ampere’s surface so, the magnetic field is zero.
But for external points, the whole current behaves as if it were concentrated at the axis only, so outside
$${B_0} = \frac{{{\mu _0}i}}{{2\pi r}}$$
Thus, the magnetic field is produced outside the pipe only.