Easy Electrodynamics Question on Field Lines

[Kyle91]

Homework Statement

Explain why the electric field is perpendicular to any conducting surfaces in static situations. Is this true in general (i.e. even for changing electric or magnetic fields)? Are there similar conditions on the direction of a magnetic field at the surface of a conductor.

The Attempt at a Solution

I know how to do the first bit regarding static electric fields, but I can't find anything online about changing electric fields.

Everything I do find says 'Always must be perpendicular', but their justification is that it wouldn't be static if it wasn't normal. Therefore I think it is possible to have non-perpendicular field lines at the surface provided the charges in the conductor aren't static.

I need some sort of justification for this (other than what I've said above) so if you could point me in the right direction it'd be greatly appreciated.

About the magnetic fields, from wikipedia -

"A magnetic field has no sources or sinks (Gauss's law for magnetism), so its field lines have no start or end: they can only form closed loops, or extend to infinity in both directions."​

Now the bit I'm not sure about, is it right to say that these magnetic field lines are perpendicular to the electric field lines near the surface of a conductor? In other words, they look exactly like equipotential lines. Take this (http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/equiv3.gif) image for example, if I were to draw in mag field lines I could trace over the dots and put arrows in a clockwise direction, right?

I'm getting confused because I'm trying to apply the right hand rule and can't think of anything curling around a vector :S

Cheers

 

[sunjin09]

The magnetic field B at the surface of conductor is tangential only from the div-free condition of B, (draw a small cylinder across the surface and knowing B=0 inside the conductor tells you vertical B=0). Because they are div-free, their field line at the surface are closed loops. But there are no other restrictions on it. (They are of course perpendicular to E field, because E field is perpendicular to the surface)