Two conducting, charged spheres

[bizonek]

Homework Statement

I have found this problem in Feynman Lectures on Physics vol. 2:

Two equal conducting spheres, one with the total charge of $$+Q$$ and the other with a total charge of $$-Q$$, are placed at some distance from each other. What is the force between them?

Homework Equations

Coulomb's Law:
$$F=k\frac{q_{1}\cdot q_{2}}{r^{2}}$$

The Attempt at a Solution

There is a tip to solve that problem by constructing an infinite number of images, so I tried to do it that way:

[PLAIN]http://img338.imageshack.us/img338/4906/rysp.jpg

X-coordinate of the n-image will be:
$$x_{n}=\frac{R^2}{d-x_{n-1}}$$
The charge we have to place in that coordinates is:
$$q_{n}=\frac{R}{d-x_{n-1}}\cdot q_{n-1}$$

Of course: $$x_{0}=0$$ and $$q_{0}=Q$$

Total force, which first sphere attract on the second, will be:
$$F_{12}=\sum{k\frac{q_{n}\cdot (-Q)}{(d-x_{n})^2}}$$


Is that correct solution or not? And how to do the last operation?

 

[anathema]

it is important to approach problems with a critical and analytical mindset. While constructing an infinite number of images may be a valid approach, it is always important to check the validity and accuracy of your solution. I would suggest double checking your calculations and equations, as well as considering alternative methods for solving this problem. Additionally, it may be helpful to consult with peers or a mentor for feedback and guidance. As for the last operation, it would depend on the final form of your solution and whether it can be simplified further. Good luck!