Question
A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere's circuital law is generalized to incorporate the effect due to the displacement current.
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Answer
According to Ampere's circuital law, $\oint\overline{\text{B}}.\overline{\text{dl}} = \mu_{o}\text{I}_{en}$
For $C_{1 }\oint\overline{\text{B}}.\overline{\text{dl}} = \mu_{o}\text{I}_{en}$
For $C_{2 }\oint\overline{\text{B}}.\overline{\text{dl}} = 0 $
There is an inconsistency in Ampere's circuital law.To explain this displacement current was incorporated.
Using Ampere's law, we find different values of $B$ for the two loops.
Hence displacement current was introduced.
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