First slide

Ampere's circuital law

Question

A current I flows along the length of an infinitely long straight thin walled pipe. Then

Moderate

A

The magnetic field is zero only on the axis of the pipe.
B

The magnetic field is different at different points inside the pipe.
C

The magnetic field at any point inside the pipe is zero.
D

The magnetic field at all points inside the pipe is the same, but not zero.

Solution

Consider a circular loop of radius r inside the tube. Then net current $(i_{net})$ enclosed by the loop is zero.
From the equation $\oint \vec{B} . \vec{dl} = μ_{0} i_{net}$
$\Rightarrow \oint \vec{B} . \vec{dl} = 0 \Rightarrow B . 2 πr = 0 \Rightarrow B = 0$

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