solve using the guassian law not green functionProve this mean value theorem: For charge-free space in the electrostatic limit, the value of the electrostatic potential φ at any point in space is equal to the average of the potential over the surface of any sphere centered on that point.Hint: Use the fact that where there are no charges ∇2φ=0. Then relate the averge φ over the surface of a shpere to the flux of electric field through the surface.Functions which satisfy Laplace's equation are called harmonic functions; harmonic functions obey the above mean value theorem (in other words, you have to prove this mean value theorem, you cannot simply say it is true because harmonic functions obey it!).

Answered: Image /qna-images/answer/8ac1d6ba-0cb8-4282-8b0d-dd4df46d5381.jpg

Answered: solve using the guassian law not green…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Question

solve using the guassian law not green function

Prove this mean value theorem: For charge-free space in the electrostatic limit, the value of the electrostatic potential φ at any point in space is equal to the average of the potential over the surface of any sphere centered on that point.

Hint: Use the fact that where there are no charges ∇²φ=0. Then relate the averge φ over the surface of a shpere to the flux of electric field through the surface.

Functions which satisfy Laplace's equation are called harmonic functions; harmonic functions obey the above mean value theorem (in other words, you have to prove this mean value theorem, you cannot simply say it is true because harmonic functions obey it!).

Expert Solution