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Electric field inside a dielectric sphere with cavity

  1. May 9, 2015 #1
    Original Problem:

    "A sphere of radius a is made of a nonconducting material that has a uniform volume charge density [PLAIN]http://jkwiens.com/2007/10/24/answer-electric-field-of-a-nonconducting-sphere-with-a-spherical-cavity/d2606be4e0cd2c9a6179c8f2e3547a85_2.gif. [Broken] A spherical cavity of radius b is removed from sphere which is a distance z from the center of the sphere. Assume that a > z + b. What is the electric field in the cavity?"

    I understand how to solve an ordinary problem like this, but what if the sphere has dielectric constant ε which is different from the cavity whose permittivity is ε0? When solving this, should I treat the imaginary small sphere with -ρ to have permittivity ε or ε0?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. May 9, 2015 #2

    mfb

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    Staff: Mentor

    The imaginary sphere has the same material as the sphere around it. Not sure if that influences the result at all.
     
  4. May 9, 2015 #3
    But when I was doing another problem which deals with calculating the self inductance of a toroid with a small gap, whose permeability is μ for the iron part and μ0 for the gap, the answer uses μ0 to calculate the B field in the gap (used "imaginary wire loop")...And the answer is definitely different using ε/ε0 in the sphere case. Still not sure why. Maybe the answer of that problem is wrong...
     
  5. May 9, 2015 #4

    mfb

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    For the toroid magnet, you don't remove something, you treat it as circle with two different materials the whole time. And you don't have a charge distribution as you have here.
     
  6. May 9, 2015 #5
    Woo that makes sense...Thanks!
     
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