# Electric field from potential and coordinate

1. Feb 20, 2009

### axgalloway

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

I am given V(x,y,z) = 3x^2 + 2y + 5 and I am given s = (5,3,1), so what is the electric field?

2. Relevant equations
V= Es

3. The attempt at a solution
I really have no idea. What I tried:

Derivative of V(x,y,z) = 6x+2
so E = 32 N/C?

Really I just don't understand the math necessary. How is it done?

2. Feb 21, 2009

### Staff: Mentor

What you really need to do is take the gradient of the potential function:

$$E = - \nabla V$$

You'll find the components of the electric field by taking the partial derivative with respect to each variable. Thus the x-component of the field will be -6x.