# Homework Help: Derive an equation for electric potential V(z) on z axis

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1. Aug 29, 2015

### jackMybrain@ru

1. The problem statement, all variables and given/known data
Hi, I am stuck with this homework. I have been asked to make an equation out of a diagram for V(z) using V=kQ/r equation, where z is a positive axis centred with four negative charges. Here is the diagram.

2. Relevant equation
E=F/q
F of point charge: F=kQq/r^2
E=kQ/r^2
V=kQq/r ~U=V*q & KE=0.5m*velocity^2

r=distant of the point from the point charge q
k=1/4*pi*[E][/0]

3. The attempt at a solution
I have already completed the (a) and (b) parts. However, for part (b) I could only make V(z)=Q/(4*pi*Enod)*r where r = 0.5*sqrt([d^2+(2Z-d)^2]) from the r12. I found r by taking all point charges distant together by saying r12 of the first 2 charges are equal and r34 of the 3rd and 4th is same. Therefore, Vtotal=KQ*[(2/r12)+(2/r34)]. But how do I make it as V(z)=-Q/pi*Enod.... because currently I am getting V(z)=-Q/8*pi*Enod(sqrt([d^2+(2Z-d)^2])).
Am I doing something wrong. Thanks for any insight or solution for the other parts would be very helpful.
And how do I do Q 1. (c),(d)& (f)??

Last edited by a moderator: Aug 29, 2015
2. Aug 30, 2015

### jackMybrain@ru

This is an easier version of my question. Please, help!! I don't know why nobody is familiar with V(z) equation or how to solve them. Because there are not many references or videos to be found by online searching. Thanks again..

3. Aug 30, 2015

### ehild

Show your derivation for r12 and r34 in detail.