# Past exam question about electrostatic field and potential

## 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

## 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

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rude man
Homework Helper
Gold Member

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

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

Isn't that just the vector calculus identity that the curl of a gradient is zero?
Yes, this is an identity.

rude man
Homework Helper
Gold Member