A charged metallic sphere A is suspended by a nylon thread another charged metallic sphere b held by an insulating centers is 10 cm as shown in Fig. 1.7(a). The resulting repulsion of A is noted (for example, by shining a beam of light and measuring the deflection of its shadow on a screen). Spheres A and B are touched by uncharged spheres C and D respectively, as shown in Fig. 1.7(b). C and D are then removed and B is brought closer to A to a distance of 5.0 cm between their centers, as shown in Fig. 1.7(c). What is the expected repulsion of A on the basis of Coulomb’s law? Spheres A and C and spheres B and D have identical sizes. ignore the sizes of a and b in comparison to the separation between their centers

Explanation

Let the original charge on spere a be q and that on b be q at a distance r beteen their centres the magnitude of the `F=(1)/(4piepsilon_(0))(qq)/(r^(2))`
neglecting the sizes of sperhers a and b in comparions to r when an identical but unchanged spere c touches a the charges redisitribute on a and c and by symmetry each sprere carries a charge `q//2` similary after d touches b the rredistributed charge on each is of the electrosatic force on each is
`F=(1)/(4pi epsilon_(0))((q//2)(q//2))/(r//2)^(2)=(1)/(4piepsilon_(0))(qq)/(r^(2))=F`
Thus the electrostatic force on a due to b remains unaltered