Electricity and magnetism/Electrostatics/The potential produced by several charges

The electric field created by several charges is the sum of the fields created by each of them separately. Now the gradient of a sum is the sum of gradients, because d(f+g)/dx = df/dx + dg/dx. The electric field created by several charges therefore derives from the sum of the electric potentials created by each of them separately. We thus prove that the electric field created by several charges also derives from a potential. Since Newton's potential is mathematically similar to Coulomb's potential, the same is true for the gravitational force. The field producing two equal and opposite charges can be represented with field lines: 267px with equipotential lines: 320px or by representing its potential as a relief: 400px We can also see the field lines in space: 640px The gravitational potential produced by the Earth and the Moon is identical to the electric potential produced by two negative electric charges which would have electric charges proportional to the masses of the Earth and the Moon: 400px The field lines are in blue, the equipotential lines in red. We can also represent this potential by an altitude field: File:Earth-moon-gravitational-potential-3d.gif