com www.GOALias.blogspot.com

www.GOALias.blogspot.comElectric Chargesand FieldsSolution Let the original charge on sphere A be q and that on B beq′. At a distance r between their centres, the magnitude of theelectrostatic force on each is given by1 qq′F =24 π ε r0neglecting the sizes of spheres A and B in comparison to r. When anidentical but uncharged sphere C touches A, the charges redistributeon A and C and, by symmetry, each sphere carries a charge q/2.Similarly, after D touches B, the redistributed charge on each isq′/2. Now, if the separation between A and B is halved, the magnitudeof the electrostatic force on each is1 ( q/2)( q′ /2) 1 ( qq′)F′= = = F4πε4πε2 20 ( r/2)0 rThus the electrostatic force on A, due to B, remains unaltered.EXAMPLE 1.51.7 FORCES BETWEEN MULTIPLE CHARGESThe mutual electric force between two charges is givenby Coulomb’s law. How to calculate the force on acharge where there are not one but several chargesaround? Consider a system of n stationary chargesq 1, q 2, q 3, ..., q nin vacuum. What is the force on q 1dueto q 2, q 3, ..., q n? Coulomb’s law is not enough to answerthis question. Recall that forces of mechanical originadd according to the parallelogram law of addition. Isthe same true for forces of electrostatic origin?Experimentally it is verified that force on anycharge due to a number of other charges is the vectorsum of all the forces on that charge due to the othercharges, taken one at a time. The individual forcesare unaffected due to the presence of other charges.This is termed as the principle of superposition.To better understand the concept, consider asystem of three charges q 1,q 2and q 3, as shown inFig. 1.8(a). The force on one charge, say q 1, due to twoother charges q 2, q 3can therefore be obtained byperforming a vector addition of the forces due to eachone of these charges. Thus, if the force on q 1due to q 2is denoted by F 12, F 12is given by Eq. (1.3) even thoughother charges are present.1 qq1 2Thus, F 12= rˆ2 124 π ε0 r12In the same way, the force on q 1due to q 3, denotedby F 13, is given by1 qq1 3F13 = rˆ2 134 πε r0 13FIGURE 1.8 A system of (a) threecharges (b) multiple charges.15