How can Eddy currents exist within a conductor if no electric field can exist inside a conductor?

In electrostatics, I learnt that the electric field inside a conductor is zero because of the free electrons moving to the surface of the conductor to decrease repulsions and ultimately decrease energy, and therefore, by Gauss’ law, the electric field inside a conductor is zero. If that is the case, how can eddy currents exist within a conductor? I know that induced electric field is non-conservative in nature and I suspect that has something to do with it, but I don't exactly know what it is.

In electrostatics, I learnt that the electric field inside a conductor is zero because ...

Note the second word you used: electrostatics. The electric field inside a conductor is zero in electrostatics. Eddy currents are not electrostatic.

A conductor obeys Ohm’s law: $$\vec J = \sigma \vec E$$. So you can certainly have an E field in a conductor in general. It is only once you add in the electrostatic condition $$\vec J=0$$ that you get $$\vec E=0$$. That condition doesn’t apply for eddy currents.

• Okay. Why is charge density zero in electrostatics? – CannedOrgi Mar 6 at 13:18
• @Rahul Vivek J is current density, not charge density. “Electrostatic” means the charges are not moving and J indicates how the charges are moving. So electrostatic means $\vec J=0$ – Dale Mar 6 at 16:34
• Oh yeah, I meant to say current density. I never realized that "electrostatic" implies that the charges don't move. Thanks, Dale! – CannedOrgi Mar 7 at 16:08