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www.GOALias.blogspot.comElectric Chargesand Fieldsspheres. When the separation between two spheres is muchlarger than the radius of each sphere, the charged spheresmay be regarded as point charges. However, the chargeson the spheres were unknown, to begin with. How thencould he discover a relation like Eq. (1.1)? Coulombthought of the following simple way: Suppose the chargeon a metallic sphere is q. If the sphere is put in contactwith an identical uncharged sphere, the charge will spreadover the two spheres. By symmetry, the charge on eachsphere will be q/2*. Repeating this process, we can getcharges q/2, q/4, etc. Coulomb varied the distance for afixed pair of charges and measured the force for differentseparations. He then varied the charges in pairs, keepingthe distance fixed for each pair. Comparing forces fordifferent pairs of charges at different distances, Coulombarrived at the relation, Eq. (1.1).Coulomb’s law, a simple mathematical statement,was initially experimentally arrived at in the mannerdescribed above. While the original experimentsestablished it at a macroscopic scale, it has also beenestablished down to subatomic level (r ~ 10 –10 m).Coulomb discovered his law without knowing theexplicit magnitude of the charge. In fact, it is the otherway round: Coulomb’s law can now be employed tofurnish a definition for a unit of charge. In the relation,Eq. (1.1), k is so far arbitrary. We can choose any positivevalue of k. The choice of k determines the size of the unitof charge. In SI units, the value of k is about 9 × 10 9 .The unit of charge that results from this choice is calleda coulomb which we defined earlier in Section 1.4.Putting this value of k in Eq. (1.1), we see that forq 1= q 2= 1 C, r = 1 mF = 9 × 10 9 NThat is, 1 C is the charge that when placed at adistance of 1 m from another charge of the samemagnitude in vacuum experiences an electrical force ofrepulsion of magnitude 9 × 10 9 N. One coulomb isevidently too big a unit to be used. In practice, inelectrostatics, one uses smaller units like 1 mC or 1 μC.The constant k in Eq. (1.1) is usually put ask = 1/4πε 0for later convenience, so that Coulomb’s law is written as1 q q1 2F =2(1.2)4 π ε0rε 0is called the permittivity of free space . The value of ε 0in SI units isε0= 8.854 × 10 –12 C 2 N –1 m –2* Implicit in this is the assumption of additivity of charges and conservation:two charges (q/2 each) add up to make a total charge q.Charles Augustin deCoulomb (1736 – 1806)Coulomb, a Frenchphysicist, began his careeras a military engineer inthe West Indies. In 1776, hereturned to Paris andretired to a small estate todo his scientific research.He invented a torsionbalance to measure thequantity of a force and usedit for determination offorces of electric attractionor repulsion between smallcharged spheres. He thusarrived in 1785 at theinverse square law relation,now known as Coulomb’slaw. The law had beenanticipated by Priestley andalso by Cavendish earlier,though Cavendish neverpublished his results.Coulomb also found theinverse square law of forcebetween unlike and likemagnetic poles.11CHARLES AUGUSTIN DE COULOMB (1736 –1806)