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Finding the Electric Field given the potential in spherical

  1. Feb 2, 2017 #1
    1. The problem statement, all variables and given/known data
    The problem statement is in the attachment

    2. Relevant equations
    E
    = -φ

    = (∂φ/∂r)er
    3. The attempt at a solution

    I am confused about how to do the derivative apparently because the way I do it gives

    E = - (∂[p*r/4πε0r3]/∂r)er = 3*(p*r)/4πε0r4er
     

    Attached Files:

  2. jcsd
  3. Feb 2, 2017 #2

    pasmith

    User Avatar
    Homework Helper

    [itex]\mathbf{r}[/itex] is not a constant.

    I would suggest staying in Cartesian coordinates so that [tex]
    \frac{\partial \phi}{\partial x_i} = \frac1{4\pi\epsilon_0} \sum_j p_j \frac{\partial}{\partial x_i}\left(\frac{x_j}{r^3}\right)[/tex] and using the results [tex]
    \frac{\partial r}{\partial x_i} = \frac{x_i}{r}[/tex] and [tex]
    \frac{\partial x_j}{\partial x_i} = \begin{cases} 1, & i = j, \\ 0, & i \neq j.\end{cases}[/tex]
     
    Last edited: Feb 2, 2017
  4. Feb 2, 2017 #3
    well if I plugged that in for r, wouldn't I just get

    E = - (∂[p*rer/4πε0r3]/∂r)er = (p*er)/2πε0r3er ?
    I haven't done vector calculus in a long time, idk if im forgetting something obvious or what
     
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