According to ohm's law j=kE, where k is conductivity.As E changes so current density j changes hence current i changes.So, if within a closed loop current i is continously changing then how can ampere's law applicable?So, electric field has to be constant.
Consider a parallel plate capacitor getting charged while connected to a battery and a resistor. Now, take Amperian loop between the plates of the capacitor. There is no flow of electrons/ions taking place in between the plates. So, in applying Ampere's law, it may appear that the magnetic field is zero (no flow of current through the loop). However, magnetic field in reality is not zero and hence Ampere's law needs correction factor here.
Ampere's law in absence of variable electric field is given by:
\(\oint {\vec B.\vec {dl} } = \mu _0 I_{in}\)
This needs to be refined when the electric field is variable like in capacitor charging case, and then one can apply Ampere's law in capacitor charging case or in any other case when the electric field is changing.
The general Ampere's law is:
\(\oint {\vec B.\vec {dl} } = \mu _0 \left( {I_{in} + \varepsilon _0 {{d\phi _E } \over {dt}}} \right)\)
Ampere's law in absence of variable electric field is given by:
\(\oint {\vec B.\vec {dl} } = \mu _0 I_{in}\)
This needs to be refined when the electric field is variable like in capacitor charging case, and then one can apply Ampere's law in capacitor charging case or in any other case when the electric field is changing.
The general Ampere's law is:
\(\oint {\vec B.\vec {dl} } = \mu _0 \left( {I_{in} + \varepsilon _0 {{d\phi _E } \over {dt}}} \right)\)
Thank you,Sir.