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

AI Thread Summary
To find the electric field from the given electric potential V(x) = 3x - 2x^2 - x^3, the correct approach involves taking the derivative of V with respect to x. The electric field E is defined as E = -dV/dx, which means the negative sign must be included in the calculation. The initial attempts at differentiation were incorrect due to the omission of this negative sign, leading to confusion about the results. The correct derivative yields E = -(3 - 4x - 3x^2), which simplifies to E = -3 + 4x + 3x^2. Understanding the relationship between potential and electric field is crucial for solving this problem accurately.
kevinr
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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.
 
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The electric field is given by

E = - \vec{\nabla}V

In this case,

E = -\frac{dV}{dx}

Your forgetting the minus sign.
 
ah ok ;) makes sense.

Thanks!
 
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