Consider two electrons approaching each other at rather fast speeds, maybe even coming close to colliding. Does gravity play any role in this event? If so, how much influence does it have? Do we need gravity in charged particles?
Answer
Gravitation is a negligible effect unless you have a large number of particles and a very small percentage of net charge.
For two protons, the electromagnetic force is $10^{36}$ times stronger than their gravitational force. But if you have a small object made up of protons and neutrons and electrons, with a total of about $10^{36}$ atoms and just one more proton than electrons, then the forces are equal. For planetary, stellar, and galactic sizes the electromagnetic force can be ignored compared to gravity, except when you have localized overcharges like around solar flares.
For atoms and molecular effects, or even electrical circuits, gravitation can just be ignored
See relative strengths of the elementary 4 forces at Wikipedia page on fundamental interaction.
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