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Homework Help: Show E=−∇ϕ

  1. Nov 1, 2014 #1
    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 [itex]E = -\nabla\phi[/itex]

    2. Relevant equations
    [itex]E = -\nabla\phi[/itex]
    [itex]V = \int{^A_B}{E\cdot{dr}}[/itex]

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

    I know its not this simple because it seems like my maths has gone around in circles. Any help please?
  2. jcsd
  3. Nov 1, 2014 #2
    You do know that V and φ are the same parameter, correct?

  4. Nov 1, 2014 #3
    Yes I do know that.
  5. Nov 1, 2014 #4


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    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?
  6. Nov 2, 2014 #5
    So, when you calculate ##\vec{E}\centerdot d\vec{r}## in terms of ##\phi##, what do you get?

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