Electric field from potential and coordinate

[axgalloway]

Homework Statement

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?

Homework Equations

V= Es

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?

 

[Doc Al]

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.

See: http://hyperphysics.phy-astr.gsu.edu/Hbase/gradi.html"