This is a question from class 12 Physics NCERT Part I:
Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. [Hint: Use the fact that work done by electrostatic field on a closed loop is zero.]
I understand that a charged surface (which is not necessarily a conductor) can have a tangential component to the electric field. I have two questions:
a) I know there's some concept I'm completely forgetting here, but does this not mean that there's a force now that can move the charges along the surface, which isn't possible in electrostatics?
b) Also, can anyone help me understand how the 'work done in a closed loop is zero' fact proves that the tangential component is continuous? Where do I take the closed loop to be?
Any help is appreciated, thank you so much.