# Finding the Electric Field given the potential in spherical

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1. Feb 2, 2017

### John004

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

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2. Feb 2, 2017

### pasmith

$\mathbf{r}$ is not a constant.

I would suggest staying in Cartesian coordinates so that $$\frac{\partial \phi}{\partial x_i} = \frac1{4\pi\epsilon_0} \sum_j p_j \frac{\partial}{\partial x_i}\left(\frac{x_j}{r^3}\right)$$ and using the results $$\frac{\partial r}{\partial x_i} = \frac{x_i}{r}$$ and $$\frac{\partial x_j}{\partial x_i} = \begin{cases} 1, & i = j, \\ 0, & i \neq j.\end{cases}$$

Last edited: Feb 2, 2017
3. Feb 2, 2017

### John004

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