Net Electric field inside a conductor=0

[varadgautam]

If the net electric field inside a conductor is zero, how come electrons flow on applying potential difference across it? What force acts on the electrons? We've been taught that
an electric field E sets up, so the force on electrons is eE (e=charge on electron).
acceleration a=eE/m (m=mass of electron)
and then they calculated drift velocity. But by Gauss' Law, Electric field inside a conductor is zero, so thre must be no force on the electrons.

 

[Meir Achuz]

E=0 in the static case after the movement of the electrons.

 

[Pythagorean]

a) that is only for a perfect conductor :)

b) given a perfect conductor, the electrons will travel only on it's surface, not inside it.

 

[BruceW]

$$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$$
(where $\rho$ is the charge density)
so this means that the divergence of the electric field is constant within the conductor. Surely this allows a constant electric field throughout the conductor?

Edit: I'm being stupid. This would only allow a constant electric field if the total charge density is zero. But I guess this is true in conductors where there are both positive and negative charges.

 

[vanhees71]

In electrostatics, i.e., in the case of time-independent fields and charge distribution and the absense of currents, the electric field in conductors, no matter whether they are ideal or resitive, must vanish because of Ohm's Law,

$$\vec{j}=\sigma \vec{E}.$$

Since $\vec{j}=0$ for $\sigma \neq 0$ one must have $\vec{E}=0.$

In any other cases, one has to determine the electric field inside conductors by the general boundary and initial conditions, necessary for the unique solution of Maxwell's Equations.

 

[BruceW]

So to directly answer the OP: If a conductor has no currents flowing through it, then there is no electric field inside the conductor. And if there is a current flowing, there generally will be an electric field.
This sound right to everyone?