Past exam question about electrostatic field and potential

[ZedCar]

Homework Statement

Using Stoke’s theorem and the identities given, ∇x∇(Scalar)=0 deduce the relationship between electrostatic field E and potential ψ at a point in space, show that E = -∇ψ

Homework Equations

The Attempt at a Solution

Does this question mean show a derivation which uses Stoke’s theorem and mathematical identities to obtain E = -∇ψ ?

Or is something else required since it states, "∇x∇(Scalar)=0 deduce the relationship between electrostatic field E and potential ψ at a point in space". I wasn't sure if by a derivation arriving at E = -∇ψ then in effect this would be illustrated.

Thanks

 

[rude man]

Can't read your question. What is ∇x∇(Scalar)=0 ?

 

[ZedCar]

Can't read your question. What is ∇x∇(Scalar)=0 ?

That's exactly the way its typed on the past exam paper ie ∇x∇(Scalar)=0

 

[Fightfish]

Can't read your question. What is ∇x∇(Scalar)=0 ?

Isn't that just the vector calculus identity that the curl of a gradient is zero?

 

[ZedCar]

Isn't that just the vector calculus identity that the curl of a gradient is zero?

Yes, this is an identity.

 

[rude man]

OK, I can't read the del sign in your posts. But OK, no problem now.

Start with the circulation integral: ∫E*ds = 0. This is a fundamental experimental observation. Then invoke Stokes' theorem to show that the curl of E must always be zero since the theorem applies to all possible closed paths.

Then invoke the fact that, in consequencxe of curl E = 0 there exists a potential function V such that E = - grad V.