- #1

Denver Dang

- 148

- 1

## Homework Statement

Hi.

This one I really am lost on :/

In my mind it seems rather easy, but I still can't figure it out.

I have been given the E-field:

[tex]

\mathbf{E}\left( t,\,\,\vec{r} \right)=\frac{\kappa }{{{\varepsilon }_{0}}}\left[ \begin{matrix}

ctx+{{x}^{2}}-{{y}^{2}} \\

cty+{{y}^{2}} \\

ctz+{{z}^{2}}-{{y}^{2}} \\

\end{matrix} \right]

[/tex]

And then I have calculated the vector potential, which gives:

[tex]\mathbf{A}=\frac{\kappa t}{{{\varepsilon }_{0}}}\left[ \begin{matrix}

{{y}^{2}} \\

0 \\

{{y}^{2}} \\

\end{matrix} \right]

[/tex]

And now I need to calculate the scalar potential

## Homework Equations

I'm thinking this one:

[tex]\mathbf{E}=-\nabla V-\frac{\partial \mathbf{A}}{\partial t}[/tex]

## The Attempt at a Solution

My problem is, that I'm not entirely sure about what to do with the scalar potential [itex]V[/itex].

Taking the derivative of [itex]A[/itex] is no problem, and adding [itex]E[/itex] and [itex]A[/itex] together is easy as well. But how is it get the scalar potential to stand alone ? Differentiate with [itex]\nabla[/itex] on both sides doesn't make sense to me.

I'm guessing it's pretty simple, but again, at the moment, I'm kinda lost :/

So any help would be appreciated.

Thanks in advance.