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The value of magenetic field produced by coduction current and displacement current are equal at the edges ofor capacitor or not?
Asked by 0987gauranshi | 04 Jan, 2022, 02:33: PM
Let us consider charging a parallel plate capacitor as shown in figure.

Let us consider an Amperian loop across the conductor .

This amperian loop can be boundary to a flat surface or a baloon like surface as shown in figure.

In the flat surface , Ampere's law is written as

...................................(1)
where Ic is conduction current.

If the balloon like surface encloses only displacement current Id inside capacitor plates then

........................(2)
Subscript S in the integral represents surface integration performed over baloon like surface

Electric field inside capacitor E is given as

where σ is charge density , Q is charge at an instant of time t and A is area of plates

.......................................(3)

From eqn.(2) and eqn.(3) , we get

...............................(4)
Above equation is same as eqn.(1)

Hence magnetic field produced by conduction current and magnetic field produced  by
displacement current at the edge of capacitor are same

Answered by Thiyagarajan K | 04 Jan, 2022, 05:10: PM

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