Why Can't I Sum Potentials in Electrostatics Problem?

[Beer-monster]

Homework Statement

I'm trying to work through revisit some basic physics and am working through some electrostatics examples (in Griffith for example). I'm currently working through the 'classic' problem for the http://en.wikipedia.org/wiki/Method_of_image_charges" i.e. a pont charge a small distance (d) from a grounded conducting plane.

I can follow through most of the steps myself but there is one part where you sum the potentials from the real and the image charge that I can't wrap my head around.

Homework Equations

The relevant sum in cylindrical co-ordinates:

$$\frac{dV}{dz} = k \left( \frac{-q(z-d)}{[r^{2}+(z-d)^{2}]^{3/2}} + \frac{q(z+d)}{[r^{2}+(z+d)^{2}]^{3/2}} \right)$$

b]3. The Attempt at a Solution [/b]

My math appears to have gotten quite rusty and I'm unsure where to start. I have a feeling there's a simple trick to it but I can't see it with how messy the sum is. Anyone have any ideas?

 

[vela]

What exactly is your question?

 

[Beer-monster]

It's embarassing but I'm blanking on how to add those together to simplify the expression. Everything I tried to get a common denominator to add together has failed, though that could be ther confusion of the messy terms.

I was wondering if someone could point me in the right direction if I'm missing something.

 

[vela]

I'd leave it as is. That's about the cleanest form you're going to get it in. In other words, it's not coming out a mess only because you're not remembering your algebra.

 

[rwisz]

I understand your frustration when trying to work through a problem and getting stuck on a particular step. In this case, it may be helpful to break down the sum into smaller parts and simplify each part individually. For example, you can start by simplifying the first term in the sum, then the second term, and finally adding them together. Additionally, it may be helpful to review the fundamental principles of electrostatics and the method of image charges to gain a better understanding of the problem. Don't be afraid to reach out for help from other resources, such as your textbook or a tutor, to guide you through the process. With persistence and a clear understanding of the concepts, I am confident you will be able to solve this problem.