Question

When using the Ampere Maxwell equation, are you supposed to integrate the flux first, or take the time derivative first. I had assumed that the integration of the flux would have to happen first, but I'm seeing someone take the time derivative first, and then integrating. I'm using the integral form of the equation. Please help me understand what I'm missing. Thank you!

Answer 1

the Ampere Maxwell equation is

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for Ampres circuital law consider a surface

for surface S₁

displacement current=0

I_D=0

so

for surface 2

I=0

conduction current entre pate A and leaves capacitor B so the current is not continuous

the displacement current between the capacitor

so the total value is