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Ok, so I know equations for force due to gravity, electricity, and magnetism, but what about the force due to the weak and strong forces? I'd like to be able to calculate where an electron is when it's in equilibrium between the coulomb force and the nuclear force.

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An electron in 'equilibruim' will be orbiting in one of the energy levels described by the Bohr model for the atom. The strong nuclear force is described by quantum chromodynamics. The weak force is described by field theories or the electro-weak unified theory, not sure about that. I don't think any of these affect the electron which is relatively far from the nucleus.
As @ten said, the electron does not feel the nuclear forces. In quantum mechanics ( which you would need in order to describe such forces ) the electron is described as feeling only the electrostatic attraction of the nucleus (and the repulsion of other electrons, etc, but it's electrostatic in nature).
Furthermore the electrons do not exist at fixed equilibrium positions. The electron can in principle exist at any radial distance from the electron, but probabilistically is most likely to exist at approximately the bohr radius.

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Other answers:

For ground-state hydrogen*
Yeah I know that they really aren't like this, but I kind of just wanted to be able to approximate it roughly in this way. I was kind of assuming this might have been how the bohr radius was determined originally. Oh well, thanks. =D
The bohr radius was determined assuming that the electron could orbit the nucleus only in circular orbits with angular momentum equal to integer multiples of planck's constant divided by 2 pi. You can derive it from there.
equating centripetal force with the coulomb attraction.
Awesome thanks.

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