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

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