Compare Electric, Magnetic Fields With Gravitational Fields



Comparison of order of magnitude of electrostatic and gravitational force

Coulombs law for electrostatic force between two pointcharges and Newtons law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses. Compare the strength of these forces by determining the ratio of their magnitudes for an electron and a proton.
The electric force between an electron and a proton at a distance r apart is:

where the negative sign indicates that the force is attractive. The corresponding gravitational force (always attractive) is

where and are the masses of a proton and an electron respectively.