1Find the average potential over a spherical surface of radius R due to a point charge q located inside (same as above, in other words, only with z < R). (In this case, of course, Laplace’s equation does not hold within the sphere.) Show that, in general, Vave = Vcenter + Qenc
1Find the average potential over a spherical surface of radius R due to a point charge q located inside (same as above, in other words, only with z < R). (In this case, of course, Laplace’s equation does not hold within the sphere.) Show that, in general, Vave = Vcenter + Qenc
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1Find the average potential over a spherical surface of radius R due to
a point charge q located inside (same as above, in other words, only with z < R).
(In this case, of course, Laplace’s equation does not hold within the sphere.) Show
that, in general,
Vave = Vcenter +
Qenc
4π±0R
,
where Vcenter is the potential at the center due to all the external charges, and Qenc is
the total enclosed charge.
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