please teach me how to prove (phy)?

2016-04-30 4:11 am
Consider a metal sphere of radius a carrying a charge +Q.
Why when inside the sphere (r<a), potential V=Q/[4(pi)ε0(a)].
Please prove it once. Thanks.

回答 (1)

2016-04-30 4:48 am
✔ 最佳答案
The potential V of the sphere on its surface
= Q/[4(pi)ε0(a)].

Because the metal sphere is a conductor, the potential at all points in the sphere are the same, and are equal to that on the surface. Hence, potential of sphere at points with r<a is also equal to Q/[4(pi)ε0(a)].

The principle behind is clear. Should there be a difference in potential between points inside the sphere and points on the surface, there would be an electric field produced. The existence of an electric field causes charges to flow (because the metal sphere is a conductor) until all points in the sphere are at the same potential. There will then be no electric field and no charges inside the sphere.


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