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Magnetic field around charging capacitor

  1. Dec 3, 2011 #1
    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[itex]\Psi[/itex]/dt)

    where μ and ε are the magnetic constant and electric constant.
    B is magnetic field, I is current, and [itex]\Psi[/itex] 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?
  2. jcsd
  3. Dec 3, 2011 #2
    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.
  4. Dec 3, 2011 #3
    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)?
  5. Dec 3, 2011 #4
    @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?
  6. Dec 3, 2011 #5
    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[itex]\Psi[/itex]/dt, so ampere's law is:

    ∫B*dl = [itex]\mu[/itex]*d[itex]\Psi[/itex]/dt

    Electric flux [itex]\Psi[/itex] = ∫E dA = E2[itex]\pi[/itex]r
    d[itex]\Psi[/itex]/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 [itex]\epsilon[/itex] according to the problem. I know I = dq/dt

    E for point change is E=kQ/r2

    Am I doing it right?
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