Coulomb's law is a fundamental law that explains electrostatic force. As long ago as 600 B.C. the Greeks knew that amber rubbed with wool would gain the property of attracting light objects. We would describe tis today as being electrically charged. In fact, the word amber means elektron in Greek.
In 1767 Joseph Priestley suggested that the law of electrical attraction was the same as that of gravitational attraction. He further concluded that the force of electrical attraction varies as the inverse square of the distance.
French engineer Charles Augustus Coulomb provided the first effective verification of Priestley's mere observation. Coulomb built a torsion balance using hairs and wires. His principle was to measure the torsion needed to bring a charged-pith-ball within various distances of another pith ball which was equally charged with electricity (the balls therefore repelled each other). Through this experiment, Coulomb founded the mathematical theory of electrical action.
Charged objects form an invisible electric force around themselves. The strength of this force depends upon a wide array of variables, including the amount of charge, distance between objects and shape of the objects. In order to simplify the whole process, Coulomb used "point sources" of charge. Point sources are charged objects which are much smaller than the distance between them. Coulomb found that for these point charges, the electrical force varies directly with the product of all charges. He concluded that the electrical force varies inversely with the square of the distance between the charges.
How is it similar to that for Universal Gravitation
Coulomb's law is very similar to the law of universal gravitation in that both equations are inversely proportional to the distance squared between the two objects being observed.
How do the two laws differ?
The two laws differ in their actual constants and the units which each deals with. Also, whereas gravity pushes objects, electrostatic energy can either repel (push) or attract (pull) an object.