Relationship between electric potential and electric field

1. Mar 15, 2015

Flotensia

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

2. Relevant equations

3. The attempt at a solution
I could find how to solve #2,4, but I don't understand what #1,3 need to me. How can I prove some functions are scalar field or vector field?

2. Mar 15, 2015

tms

The first step would be to find out what scalar and vector fields are. Once you do that, the rest should be fairly obvious.

3. Mar 15, 2015

Flotensia

Scalar field means the function of points associating scalar value. Is it clear?Then should I do rotational transformation to prove?

4. Mar 15, 2015

tms

I think you're trying to say that a scalar fields associates a scalar with each point in space, which is correct. So you have to show (show, not prove) that the potential does just that. You shouldn't need to go to the trouble of doing any transformations.

5. Mar 15, 2015

Flotensia

Don't we have to show the quantity of point is scalar or vector??

6. Mar 15, 2015

tms

You can tell that by inspection. There is nothing but scalars in #1. In #3 the result is obviously a vector, since it is a gradient, which is a vector by definition.

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