Are electric field lines always perpendicular to a conductor's surface? I know that in a conductor body, in an electrostatic situation (Where $\vec E=0$ in the interior), the E field must be perpendicular to the surface outside because it is solely generated by electric charges and therefore it is conservative. Due to this, the line integral $\int \vec E \cdot d\vec l$ must be zero for any closed path partially in and partially out of the body. This prohibits any tangential component.
My question is: Does this still stand for E fields produced by changing magnetic fields? ie. A neutral body being hit by a EM wave, or the same body being near a solenoid with changing current. My intuition tells me it should not stand, since those E fields are non-conservative according to Faraday's law, so the argument that the line integral must be zero is not enough. Moreover, it is not even an electrostatic situation, so could this be generalized (The title of the post)?
 A: It is indeed possible for the E field lines to be non-orthogonal to the surface of a conductor with finite conductance.
Remember, if the E field is derived from a scalar potential, $\phi$, then the E field being perpendicular to the surface of the conductor implies that the surface is  equipotential. So there are two ways to make the E field non-parallel to the conductor:

*

*have $-\frac{\partial \mathbf A}{\partial t}\ne 0$ so that the E field is not derived only from a scalar potential


*have $ \phi$ be spatially non-constant on the conductor surface so that even the static E field is non-perpendicular
Case 1) can be achieved using an external time-varying magnetic field, as you suggested. Case 2) can be achieved simply by having a current in a conductor with finite conductivity.
Here is a paper that describes a semi-quantitative approach for determining the surface charge on a conductor based exactly on how much the E-field “bends” at the surface.
A semiquantitative treatment of surface charges in DC circuits. Rainer Mueller. Am. J. Phys. 80 (9), September 2012. http://dx.doi.org/10.1119/1.4731722
