# Electric field given electric potential

1. Feb 21, 2008

### 743344

[SOLVED] electric field given electric potential

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

The electric potential in a region of space is V = ( 210 x^{2} - 170 y^{2} ) V, where x and y are in meters.

What is the strength of the electric field at ( 1.00 m, 3.00 m ) ?

2. Relevant equations

E = -dV/ds

3. The attempt at a solution

1. i know i have to find the derivative of the that given equation but i can't figure out where to start....because there are two different variable given....and i don't know in term of which variable i have to find the derivative

2. Feb 21, 2008

### Kurdt

Staff Emeritus
The E-field is a vector quantity and is given by the negative gradient of the potential.

$$\mathbf{E} = -\nabla V$$

the $\nabla$ operator is:

$$\nabla = \frac{\partial}{\partial x} \mathbf{\hat{i}} + \frac{\partial}{\partial y} \mathbf{\hat{j}} +\frac{\partial}{\partial z} \mathbf{\hat{k}}$$

Last edited: Feb 21, 2008
3. Feb 22, 2008

thank you