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I`ve been looking for this for some time now: I have two thin shells (S1 and S2) of radii R1 and R2, charged negatively C1 and C2 respectively, separated in space by a distance D. What is the force exerted by S1 on S2? (For my purposes, the charge can remain constantly distributed on the shell. Non-conductor, I'm guessing.)

What do I have to read to learn this? I know Coulomb's equation (F=kQ1Q2/d^2). (If relevant, I need this to emulate repulsion in a very crude ion simulation, where the attraction is emulated by considering the ions point charges. Considering the electron shells as points would be great, but obviously doesn't work... that's when the sphere approximation should do the trick.) Thank you in advance.

sammy gerbil
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Jorge Al Najjar
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1 Answers1

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As the comments tried to explain, if you can indeed treat your system as two conducting shells whose charge distribution is not affected by the presence of the other charge, then you can simply consider the charge localized at the center of each sphere, and calculate the Coulomb force in the normal way.

So if you have radii $R_1$ and $R_2$ and a separation $D$, then the distance between the centers is $R_c=R_1+R_2+D$ and the force is

$$F = \frac{C_1 C_2}{4\pi\epsilon_0 R_c^2}$$

You already said

a very crude ion simulation, where the attraction is emulated by considering the ions point charges

It turns out that the Shell theorem (which is valid for any situation where the inverse square law holds) means that, under the assumption that the spherical charge distribution remains uniform, the "point charge at the center" assumption is exactly valid.

Floris
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