Subjective Type

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.

Solution

We know, $$\displaystyle \int B \times dl = \mu_0 i$$. Theoritically $$B = 0$$ at A
If, a current is passed through the loop PQRS, then
$$B = \dfrac{\mu_0 i}{2 (\ell + b)}$$ will exist in its vicinity.
Now, As the $$\vec{B}$$ at A is zero. So there'll be no interaction
However practically this is not true. As a current carrying loop, irrespective of its near about position is always affected by an existing magnetic field.

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