Deriving the Electric Field from the Electric Potential: A Calculus Approach

[kevinr]

Homework Statement

The potential as a function of position in a region is given by V(x) = 3x - 2x^2 - x^3. (x in meters and V in volts). Find equation for electric potential field.

Homework Equations

v = integral(E * dr)

The Attempt at a Solution

I tried taking the derivative of v to get E but it keeps says I am missing something. So first i tried, 3-4x-3x^2 but its off by a multiple and than i figured since v is the integral of E * displacement --> meaning the derivative of V is E so i got what i got before and decided to divide by X which got me 3/x - 4 - 3x which also didnt work.

Im not sure quite what to do.

 

[buffordboy23]

The electric field is given by

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

In this case,

$$E = -\frac{dV}{dx}$$

Your forgetting the minus sign.

 

[kevinr]

ah ok ;) makes sense.

Thanks!