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Electric field

  1. Jul 12, 2008 #1

    Two spherical shells where the inner has a radius a and the outer a radius of b. The inner has a total charge of -Q whereas the outer shell has a total charge +Q. The question is to calculate the electric field intensity everywhere in space.
    My question is now, how do I choose the limits for example [tex] a \leq R \leq b [/tex] I have two examples below

    No point charge in the middle

    [tex] E = 0, 0 \leq R \prec a [/tex] (not equal to a)

    [tex] E = -\frac{Q}{4\pi\epsilon_{o}R^3} \bold{R} [/tex] [tex] a \leq R \leq b [/tex]

    [tex] E = 0, b \prec R \prec \infty [/tex]

    A point charge in the middle

    [tex] E = \frac{Q}{4\pi\epsilon_{o}R^3} \bold{R} [/tex] [tex] 0 \prec R \leq a [/tex] why set equal to a here and not when there aint no point charge in the middle?

    [tex] E = 0 [/tex] [tex]a \prec R \prec b [/tex]

    [tex] E = \frac{Q}{4\pi\epsilon_{o}R^3} \bold{R} [/tex] [tex] b \leq R \prec \infty [/tex]
  2. jcsd
  3. Jul 12, 2008 #2
    A point within a spherical shell experiences 0N/C. For R between a and b, inner shell is effective and outer shell's net effect is 0N/C...this works for even insulators so long as charge is evenly distributed across the shell (question didn't specify whether it was a conductor or something else). If the thickness of the shells is negligible, then you could consider the effect of the inner shell as that due to a point charge.
    Last edited: Jul 12, 2008
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