Question

Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible.

Answer 1

Half of the loop PQRS is in the region of magnetic field and half in the area of zero magnetic field.

Let us consider a current carrying circular wire, due to which there is uniform magnetic field in the region.

Take a point A inside the loop PQRS in the region where B = 0

According to Ampere's circuital law,
$\int \mathrm{B}.dl={\mu }_{0}i$

If there is current enclosed by the loop PQRS, then magnetic field B cannot be 0.

Whereas, we have taken the magnetic field at point A to be zero.

Thus, such a field is not possible.