Magnetic field around charging capacitor

[chronokinetic]

Hi everyone, I'm doing a problem that involves two circular capacitor plates with radius R connected to wires running current I (as in a circuit), and need to find the magnetic field at three different regions between the two plates as a function of r, radial distance from the center of the two plates.

Using Ampere's Law, ∫B*dl = μ(I +εd\Psi/dt)

where μ and ε are the magnetic constant and electric constant.
B is magnetic field, I is current, and \Psi is flux of electric field (between the two cap. plates, I 'spose).

I figured the best loop to integrate over is a circle (parallel to and in between the two plates).

How will I go about it from here?

 

[Naty1]

If those plates are parallel, That exact problem is an example in my (old) edition of Halliday and Resnick PHYSICS FOR STUDENTS OF SCIENCE AND ENGINEERING

E is constant between the plates, neglecting fringe effects.

 

[chronokinetic]

Thanks, I know the E is uniform, but how can you find B as a function of r ("r"adial distance away from center of plates)?

 

[Acut]

@chronokinetic: The current is charging the capacitor, therefore there is a change in the E field of the capacitor. How will that affect the displacement current?

 

[chronokinetic]

what is the displacement current? I don't know what it is.
As current I charges capacitor q, the e field should change, meaning the electric flux through a circle between the plates also increase. There is no current between the plates so I=0, but there is d\Psi/dt, so ampere's law is:

∫B*dl = \mu*d\Psi/dt

Electric flux \Psi = ∫E dA = E2\pir
d\Psi/dt = ?

How do I get E as a function of time? The distance between the plates is small so E can be written with q, A, and \epsilon according to the problem. I know I = dq/dt

E for point change is E=kQ/r²

Am I doing it right?