- #36
Doc Al
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If you think you have shown that electrostatic equilibrium does not imply zero electric field everywhere within a conductor, you would be wrong.
When we speak of conductors and electrostatic equilibrium, we are talking about all the electrons--not just those on the surface.Ulysees said:As shown below, E-field can be non-zero even though all charges are in equilibrium. You could do it with 4 electrons, or with 4000000000 electrons. The idea is the same, between electrons the field is non-zero.
The point of the shell theorem is that the field from a uniform shell of charge is everywhere zero inside the shell.Now the Shell Theorem of gravity likewise for electrostatics predicts that with enough charges evenly distributed on the surface the total field inside adds up to zero. But it does not add up to zero on the surface, between charges. The point is, equilibrium of charges does not imply zero electric field everywhere, only where each charge is.
You seem to think that if you put a charge on a conducting cube, that all the charge would end up at the corners. Not so! (If you think I'm wrong, provide a standard reference.)The field inside can be calculated numerically for any conductor based on the relation between surface curvature and charge density. For most charged conductors, the sum will NOT be zero. Take a cube for example. All charge goes to the corners of the cube. This is predicted by the relation between curvature and charge density. Shall I draw a cube and the related 6 E-field components?
Doc Al said:When we speak of conductors and electrostatic equilibrium, we are talking about all the electrons--not just those on the surface.
The point is, equilibrium of charges does not imply zero electric field everywhere, only where each charge is.The point of the shell theorem is that the field ...
You seem to think that if you put a charge on a conducting cube, that all the charge would end up at the corners.