Electric field Difference between Electrostatics and Electrodynamics

[fog37]

Hello everyone,
I have been pondering on the behavior of the E field in conductors.

In electrostatics (where the charges are not moving):

a) Electric fields are time- independent but position-dependent
b) Electric fields are always zero inside a charged or uncharged conductor. At the conductor surface, the E field is nonzero and perpendicular to the surface itself. For example, a neutral conductor immersed inside a static E field will have zero internal E field, induced surface charged and nonzero, perpendicular E field at the surface

(interestingly, a static magnetic field $B$ can penetrate inside a conductor, so we cannot shield the conductor's interior from it).

What about in electrodynamics where charges are moving, charge densities are time-varying, and the electric field $E(r,t)$ depends on time?

For example, does a conductor immersed inside a time varying E field still have a zero internal E field?
Are there situations, in electrodynamics, in which a conductor has a nonzero internal E field?

In electrodynamics, both E and B fields are always present together...

Thank you!

 

[fog37]

I would add that electric field lines never cross in electrostatics and electrodynamics.

In electrostatics, E field lines start on positive charges and end on negative charges...I think it is true also in electrodynamics where E field lines can also form closed loops that do not start/end on any charge

 

[rude man]

Are there situations, in electrodynamics, in which a conductor has a nonzero internal E field?

If it's a perfect conductor, no net electric field is possible inside it, not even if there is current flowing in it.

However, even in a perfect conductor there can exist two equal and opposite E fields. This can happen when an emf is generated. For example, in a perfect conductor of length L moving with velocity v perpendicular to a constant B field there is emf generated = BLv. vB constitutes effectively an E field. This becomes obvious if you imagine yourself sitting on the moving conductor; to you there is no v so no Lorentz force. The only possibility is an E field = v x B. To counteract the vB field an electrostatic field comprising free charge concentrated near both ends of the conductor is also generated in the opposite direction. Equilibrium is reached when the magnitudes of the two fields are equal.