Finding the Electrical Field from the Electric Potential

[Gramma2005]

I am trying to solve this problem:

The electric potential in a region of space is V = 210x^2 - 270y^2, where x and y are in meters. Find the E-field at (3m, 1m)

So I started with:

$$E = \frac{V}{d}$$

so then I plugged x and y into the electric potential equation and got

V= -200 Volts

Then I multiplied it by the distance $$d=\sqrt{x^2+y^2}$$

Unfortunately this is not the right answer. Perhaps someone could show me where I went wrong

Thanks

 

[phucnv87]

$$\vec{E}=-\vec{gradV}$$

 

[Gramma2005]

what is $$\vec{gradV}$$?

 

[Mindscrape]

If you used partial derivatives that would help you out.

 

[dicerandom]

$$\vec{E} = -\vec{\nabla}V$$$$\vec{\nabla} \equiv \frac{\partial}{\partial x} \hat{\mathbf{x}} + \frac{\partial}{\partial y} \hat{\mathbf{y}} + \frac{\partial}{\partial z} \hat{\mathbf{z}}$$