Answer to Question #202507 in Electricity and Magnetism for Dave

Question

I have a problem where two charged spheres repell each other, and as they do so compress springs. Solving for the k of the springs using force analysis is simple and results in a k value of about 55 N/m. If however you try to solve using conservation of energy you get a very different result at around 439 N/m. I can't see where either solution is incorrect but also can't resolve the difference:

Two spheres 8cm apart are each charged with 2.5 x 10^-6C. They come to rest 16cm apart. Find k.

Answer 1

$$k_C\frac{q^2}{x'^2}=0.5k(x'-x)\\9\cdot10^9\frac{(2.5\cdot10^{-6})^2}{0.16^2}=0.5k(0.16-0.08)\\k=55\frac{N}{m}$$

Energy can be dissipated but the forces needs to be equal for equilibrium.