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Electric Potential of grounded hollow metal sphere

  • Thread starter ti-84minus
  • Start date
  • #1

Homework Statement


There is a solid metal ball of radius 'a' (with charge Q) that is placed inside a hollow metal sphere (inner radius = 'b', outer radius = 'c'). The metal sphere is grounded (so V = 0 at r = c).
a) Find the electric potential V everywhere.
b) Find the charge on the metal shell at r = c and r = b.

Homework Equations


V = U/q0.
V = [itex]\frac{1}{4\pi\epsilon_{0}}\int\frac{dq}{r}[/itex]

The Attempt at a Solution


I considered the problem case by case:
r<a : V = [itex]\frac{Q}{4\pi r\epsilon_{0}}[/itex]

a<r<b
b<r<c
r>c

Would the other three cases have the same result, since electric field is zero when b<r<c and r>c? (actually, when r>c, IS the electric field zero, since the sphere is grounded?)

Thanks for your help!
 

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