1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

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

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    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?

    Chet
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted