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However, Coulomb's law can be proven from Gauss's law if it is assumed, in addition, that the electric field from a point charge is spherically symmetric (this assumption, like Coulomb's law itself, is exactly true if the charge is stationary, and approximately true if the charge is in motion).
where r is the distance between the point charges q and Q, and q and Q are the charges (not the absolute values of the charges—i.e., an electron would have a negative value of charge when placed in the formula). The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula.
The electric potential arising from a point charge, Q, at a distance, r, from the location of Q is observed to be =, where ε 0 is the permittivity of vacuum [4], V E is known as the Coulomb potential.
Alternatively the electric field of uniformly moving point charges can be derived from the Lorentz transformation of four-force experienced by test charges in the source's rest frame given by Coulomb's law and assigning electric field and magnetic field by their definition given by the form of Lorentz force. [24]
Coulomb's law states that: [5] The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. The force is along the straight line joining them.
Thus, the electric field is a complete representation of the influence of the far-away charges. Alternatively, introductory treatments of magnetism introduce the Biot–Savart law, which describes the magnetic field associated with an electric current. An observer at rest with respect to a system of static, free charges will see no magnetic field.
Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The charge of an antiparticle equals that of the corresponding particle, but with opposite sign.
Similar to point masses, in electromagnetism physicists discuss a point charge, a point particle with a nonzero electric charge. [6] The fundamental equation of electrostatics is Coulomb's law , which describes the electric force between two point charges.