Two objects are identical and small enough that their sizes can be ignored relat

Question

Two objects are identical and small enough that their sizes can be ignored relative to the distance between them, which is 0.39 m. In a vacuum, each object carries a different charge, and they attract each other with a force of 1.5 N. The objects are brought into contact, so the net charge is shared equally, and then they are returned to their initial positions. Now it is found that the objects repel one another with a force whose magnitude is equal to that of the initial attractive force. What is the initial charge on each object? (Note: there are two possible pairs of answers, but assume q1 to be the larger number.)

Explanation / Answer

Separation r = 0.39 m Attractive force F = 1.5 N Let the initial charges on each object be q and q ' We know F = Kqq' / r 2          Kqq' = F r 2             qq' = F r 2 / K Where K = Coulomb's constant                 = 8.99 x 10 9 Nm 2 / C 2 Subsitute values we get q q' = 2.537 x 10 -11             -------( 1) After contact : -------------- Charge on each object Q = ( q+ q' ) / 2 Repulsive force F ' = F                               = 1.5 N We know F ' = KQ 2 / r 2 From this Q = r [ F ' / K ]                     = 5.037 x 10 -6 C          q + q ' = 2 x 5.037 x 10 -6 C                     = 10.07 x 10 -6 C        -----( 2) ( q- q') 2 = ( q + q') 2 - 4qq'               = 3.279 x10 -14 q - q ' = 0.181 x 10 -6 C      -----( 3) [eq( 2) + eq( 3) ]/ 2 ==> q = 5.125 x10 -6 C and q ' = -4.944 x 10 -6 C     Since one is negative and other is positive so, they are attractive

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