Simple Point Charge Potential Problem

[dgreenheck]

Homework Statement

There are two point charges aligned on the X-axis. Charge A is a distance -d/2 from the origin and Charge B is a distance d/2 from the origin. What is the potential at a distance z above the center of the charge distribution?

To further clarify
Charge A location at (-d/2,0)
Charge B location at (d/2,0)
Point of analysis at (0,z)

Homework Equations

V(r) = $\frac{1}{4\pi\epsilon\stackrel{}{0}}$$\sum\frac{q\stackrel{}{i}}{r\stackrel{}{i}}$

The Attempt at a Solution

I'm confused because I'm getting 0 and the answer should be non-zero. There is no direction information carried in r, correct? Because it's just supposed to be the distance to point (0,z) which is $\sqrt{z\stackrel{2}{}+(\frac{d}{2})\stackrel{2}{}}$. And since the charges are of opposite sign, the sum will cause them to cancel out. Obviously my understanding of the summation is wrong here so if someone could point me in the right direction that would be very helpful. Thanks

 

[PeterO]

1. Homework Statement
There are two point charges aligned on the X-axis. Charge A is a distance -d/2 from the origin and Charge B is a distance d/2 from the origin. What is the potential at a distance z above the center of the charge distribution?

To further clarify
Charge A location at (-d/2,0)
Charge B location at (d/2,0)
Point of analysis at (0,z)

Homework Equations

V(r) = $\frac{1}{4\pi\epsilon\stackrel{}{0}}$$\sum\frac{q\stackrel{}{i}}{r\stackrel{}{i}}$

The Attempt at a Solution

I'm confused because I'm getting 0 and the answer should be non-zero. There is no direction information carried in r, correct? Because it's just supposed to be the distance to point (0,z) which is $\sqrt{z\stackrel{2}{}+(\frac{d}{2})\stackrel{2}{}}$. And since the charges are of opposite sign, the sum will cause them to cancel out. Obviously my understanding of the summation is wrong here so if someone could point me in the right direction that would be very helpful. Thanks

I "bolded" a couple of parts of your original post.

Are these charges equal in magnitude? Are these charges of the same sign or opposite sign?

 

[dgreenheck]

The charges are of opposite sign and of equal magnitude.