# Past exam question about electrostatic field and potential

1. May 15, 2013

### ZedCar

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. May 16, 2013

### rude man

3. May 16, 2013

### ZedCar

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

4. May 16, 2013

### Fightfish

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

5. May 16, 2013

### ZedCar

Yes, this is an identity.

6. May 16, 2013