Show E=−∇ϕ

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1. Nov 1, 2014

girlinphysics

1. The problem statement, all variables and given/known data
Two points A and B are separated in space by distance dr.
A has coordinates (x,y,z) and B has coordinates (x+dx, y+dy, z+dz).
Using the definition of potential difference, show $E = -\nabla\phi$

2. Relevant equations
$E = -\nabla\phi$
$V = \int{^A_B}{E\cdot{dr}}$

3. The attempt at a solution
With the two formulas listed above, I think I can find V, taking $E = (\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})$ from the question which means simply $V = (x,y,z)$. Since the del operator is $(\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})$, applying that to V you get $E = (\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})$.

I know its not this simple because it seems like my maths has gone around in circles. Any help please?

2. Nov 1, 2014

Staff: Mentor

You do know that V and φ are the same parameter, correct?

Chet

3. Nov 1, 2014

girlinphysics

Yes I do know that.

4. Nov 1, 2014

vela

Staff Emeritus
What you wrote doesn't really make sense. For one thing, potential is a scalar, so claiming V=(x,y,z) is nonsense. And what is $E = (\frac{d}{dx}, \frac{d}{dy}, \frac{d}{dz})$ supposed to mean?

5. Nov 2, 2014

Staff: Mentor

So, when you calculate $\vec{E}\centerdot d\vec{r}$ in terms of $\phi$, what do you get?

Chet