Computing Electric Field From The Potential

1. Sep 23, 2011

faint545

Hi all. I'm having a very hard time understanding this portion of Physics so please bear with me.

The furthest I got with this problem is deciding to use the sum of the potentials at each point to calculate the potential of the system. Something like...

$\frac{kq_{1}}{r_{1}}$ + $\frac{kq_{2}}{r_{2}}$ + $\frac{kq_{3}}{r_{3}}$

I think that's the right approach since they are point charges. But now, I'm completely stuck and I don't know what I should do next... Please help!

2. Sep 23, 2011

SammyS

Staff Emeritus
What are the values of r1, r2, and r3 at position x along the x-axis ?

3. Sep 23, 2011

faint545

Here's what I've done in regards to your question... I hope im on the right track...

Last edited by a moderator: May 5, 2017
4. Sep 23, 2011

SammyS

Staff Emeritus
$\sqrt{x^2+a^2}\ne x+a$

However, $\sqrt{x^2+(-a)^2}=\sqrt{x^2+a^2}\,.$

r3 = | x - a | . If x > a then |x - a| = x -a . Otherwise, |x - a| = a - x .

So, V(x) = ?

5. Sep 24, 2011

faint545

So I suppose $V(x) = kq(\frac{2}{\sqrt{x^{2}+a^{2}}} + \frac{1}{a-x})$ if $x < a$ and $V(x) = kq(\frac{2}{\sqrt{x^{2}+a^{2}}} + \frac{1}{x-a})$ if $x > a$.

I think I can compute $E_{x}(x)$ from here.. Thanks for all your help!

6. Sep 24, 2011

SammyS

Staff Emeritus
Looks good !