Madison Square Garden | Times Square | Tiananmen Square protests of 1989 | Trafalgar Square | Square | Leicester Square | Tiananmen Square | Red Square | A Nightingale Sang in Berkeley Square (song) | A Nightingale Sang in Berkeley Square | Square Enix | Soho Square | Rittenhouse Square | Union Square | Harvard Square | Tompkins Square Park | Thompson Square | Root mean square | Washington Square Park | Syntagma Square | Square (company) | Russell Square | Merrion Square | Independence Square | Hanover Square, London | Fitzroy Square | Cathedral Square | Taksim Square | square | Market Square Arena |
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 hydrogen atom is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law of electrostatics, another inverse square central force.
Two examples are Gauss' law (in electrostatics), which follows from the inverse-square Coulomb's law, and Gauss' law for gravity, which follows from the inverse-square Newton's law of universal gravitation.
Euler's problem also covers the case when the particle is acted upon by other inverse-square central forces, such as the electrostatic interaction described by Coulomb's law.
In fact, any "inverse-square law" can be formulated in a way similar to Gauss's law: For example, Gauss's law itself is essentially equivalent to the inverse-square Coulomb's law, and Gauss's law for gravity is essentially equivalent to the inverse-square Newton's law of gravity.
On the other hand, if we relax the conditions, and require only that the field everywhere outside a spherically symmetric body is the same as the field from some point mass at the centre (of any mass), we allow a new class of solutions given by the Yukawa potential, of which the inverse square law is a special case.
Determining the force for different charges and different separations between the balls, he showed that it followed an inverse-square proportionality law, now known as Coulomb's law.