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www.GOALias.blogspot.comPhysicswhich again is the Coulomb force on q 1due to q 3, even though othercharge q 2is present.Thus the total force F 1on q 1due to the two charges q 2and q 3isgiven asF 1 qq 1 qq= F + F = r ˆ +r ˆ(1.4)1 21 31 12 13 2 12 2 134πε0 r12 4πε0r13The above calculation of force can be generalised to a system ofcharges more than three, as shown in Fig. 1.8(b).The principle of superposition says that in a system of charges q 1,q 2, ..., q n, the force on q 1due to q 2is the same as given by Coulomb’s law,i.e., it is unaffected by the presence of the other charges q 3, q 4, ..., q n. Thetotal force F 1on the charge q 1, due to all other charges, is then given bythe vector sum of the forces F 12, F 13, ..., F 1n:i.e.,1 ⎡qq1 2qq1 3qq ⎤1 nF1 = F12 + F ˆ ˆ ˆ13+ ...+ F1n = ⎢ r2 12+ r2 13+ ... + r2 1n⎥4πε0 ⎣ r12 r13 r1n ⎦= q∑ q4r (1.5)πn1 iˆ2 1iε 0 i = 2 r1iThe vector sum is obtained as usual by the parallelogram law ofaddition of vectors. All of electrostatics is basically a consequence ofCoulomb’s law and the superposition principle.Example 1.6 Consider three charges q 1, q 2, q 3each equal to q at thevertices of an equilateral triangle of side l. What is the force on acharge Q (with the same sign as q) placed at the centroid of thetriangle, as shown in Fig. 1.9?16EXAMPLE 1.6FIGURE 1.9Solution In the given equilateral triangle ABC of sides of length l, ifwe draw a perpendicular AD to the side BC,AD = AC cos 30º = ( 3/2) l and the distance AO of the centroid Ofrom A is (2/3) AD = (1/ 3 ) l. By symmatry AO = BO = CO.