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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.

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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?

Electrostatics is not electromagnetism without forces; it's electromagnetism without relative motion, or, in other words, electromagnetism where all net forces are zero. In the case of a charged surface, there is also a force holding the charges in place, which is able to counteract the force from the tangential electric field. If there wasn't such a force, then the charged surface would be a conductor and an electric field across it wouldn't be possible, as the charges would rearrange themselves to cancel it out.

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  • $\begingroup$ Thank you! I really understand this much better. Can you help me with the second part of the question? Specifically, where should I take the closed loop to be? $\endgroup$ – laksheya Aug 16 at 9:29

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