HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q51 Solution: Sometimes we show an idealised magnetic field which is uniform…

QPages 249-253: Q51: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q51 Solution: Sometimes we show an idealised magnetic field which is uniform…

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If a magnetic field is uniform inside a region and zero outside, the line integral around a closed loop that crosses the boundary is non‑zero even when no current is enclosed. Ampere’s law requires ∮B·dl = μ0 I_enclosed, so I_enclosed = 0 forces the integral to vanish. Therefore an abrupt drop to zero is impossible unless a surface current is present.

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.

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**Answer:** A uniform field that drops abruptly to zero is not possible. **Step-by-Step Explanation:** Using Ampere's law on path PQRS (partly in field, partly out):

\oint \vec{B} \cdot d\vec{l} = \mu_0 i_{enclosed}

. If the field is uniform inside and zero outside, the line integral is non-zero even when no current is enclosed, which violates Ampere's law. Hence, such a field is impossible.

QPages 249-253: Q51: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q51 Solution: Sometimes we show an idealised magnetic field which is uniform…

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