The value of magenetic field produced by coduction current and displacement current are equal at the edges ofor capacitor or not?

### Asked by 0987gauranshi | 4th Jan, 2022, 02:33: PM

Expert Answer:

###
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 I_{c} is conduction current.
If the balloon like surface encloses only displacement current I_{d} 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

_{c}is conduction current.

_{d}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 | 4th Jan, 2022, 05:10: PM

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