Question

What is the inconsistency of Ampere's Law?

Answer 1

Ampere's law inconsistency:

According to Maxwell, ampere's law is only applicable for constant current or when the electric field does not vary the time. Describe a parallel plate capacitor being charged by a battery to demonstrate this contradiction. While charging, a variable current flows across connected wires using amperes law for loops ${\mathrm{l}}_1$ and ${\mathrm{l}}_2$.

${\oint }_{{\mathrm{l}}_1}\overrightarrow{\mathrm{B}}·\overrightarrow{\mathrm{dl}}={\mathrm{\mu }}_0\mathrm{i}$

But,

${\oint }_{{\mathrm{l}}_2}\overrightarrow{\mathrm{B}}·\overrightarrow{\mathrm{dl}}=0$

When there is no current flowing between the plates. In practice, though, a magnetic field is seen between the plates.

Hence, the ampere's law fails that is ${\oint }_{{\mathrm{l}}_1}\overrightarrow{\mathrm{B}}·\overrightarrow{\mathrm{dl}}={\mathrm{\mu }}_0\mathrm{i}$.