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Current Electricity

Question
CBSEENPH12039263

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. 

Solution

When AC current is passed through capacitor, current moves from one plate to another. According to Ampere’s circuital law, a magnetic field has to exist between the plates of the capacitor for the current transfer to happen. So, Maxwell modified Ampere’s circuital law with the help of continuity equation.
The modified Ampere’s law by Maxwell is given by,
contour integral straight B with rightwards harpoon with barb upwards on top. straight space dl with rightwards harpoon with barb upwards on top straight space equals straight space straight mu subscript straight o straight i straight space plus    straight mu subscript straight o straight epsilon subscript straight o dϕ subscript straight E over dt
space space space space space space space space space space space
space space space space space space space space space space space space equals straight space straight mu subscript straight o straight space left parenthesis thin space straight i straight space plus straight space straight i subscript straight D right parenthesis  

where, iDstraight epsilon subscript straight o dϕ subscript straight E over dtstraight epsilon subscript straight o dϕ subscript straight E over dt, is called the Displacement current.

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