# Homework Help: Electric Field and Potential

1. Feb 16, 2012

### btpolk

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

Derive the electric field for the potential function V= -x*y^2+z

2. Relevant equations

V=-∫Eds

3. The attempt at a solution

x*y^2-z=∫Eds

d/ds(x*y^2-z)= E*s

(y^2)dx/ds+(2y*x)dy/ds-dzds=E*s

I'm stuck at this point and I'm not really sure if I'm going in the right direction.

2. Feb 16, 2012

### ehild

The electric field is negative gradient of the potential function. Do you know what the gradient is?

ehild

3. Feb 16, 2012

### btpolk

All I was given is whats in the initial question. Should I just divide the s over and call it a day?

4. Feb 16, 2012

### btpolk

On the second step what if I multiplied both sides by s then divided by s^2 to get E by itself?

5. Feb 16, 2012

### ehild

E is the electric field, and it is a vector, having x, y, z components. You get these components as negative partial derivatives of the potential function.

Ex=-∂V/∂x; Ey=-∂V/∂y; Ez=-∂V/∂z.

ehild

6. Feb 16, 2012

### btpolk

So in vector form would it be <y^2,2xy,1> = E ?

7. Feb 16, 2012

### ehild

There is a minus in front of the z component.

ehild