In the figure three Identical conducting spheres initially have the following ch
ID: 2306733 • Letter: I
Question
In the figure three Identical conducting spheres initially have the following charges: sphere A, 2Q; sphere B, -7Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is mu C h larger than the spheres. Two experiments are conducted. In experiment 1, sphere C is touched to sphere A and then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same Initial states, the procedure is reversed: Sphere C is touched to sphere B and then (separately) to sphere A, and then it is removed. What is the ratio of the electrostatic force between A and B at the end of experiment 2 to that at the end of experiment 1?Explanation / Answer
when two spheres let be 1 and 2 touch each other ; the sphere shares total charge between them Q1+Q2 / 2
in experiment 1 sphere C is touched to sphere A ; there by reducing the charge on sphere A to half the initial value
before touching charge on C = 0 charge on A = +2Q
after touching charge on C = +Q charge on A = +Q
now sphere C is touched with B
after touching charge on C = +Q-7Q /2 = -3Q charge on B = -3Q
Force F1 between A and B after experiment 1
F = k Qa * Qb / d^2 with k - coloumb constant
= k Q* - 3 Q / d^2
= - k 3Q^2 /d^2 attractive force
in experiment 2 sphere C is first trouched to sphere B ; there by reducing the charge on sphere B to half the initial value
before touching charge on C = 0 charge on B = -7Q
after touching charge on C = -3.5Q charge on B = -3.5Q
now sphere C is touched with A
before touching charge on C = -3.5Q charge on A = +2Q
after touching charge on C = -3.5Q +2Q /2 = -0.75Q charge on A = -0.75Q
Force F2 between A and B after experiment 2
F2 = k Qa * Qb / d^2 with k - coloumb constant
= k * -0.75Q *-3.5 Q / d^2
= k * 2.625Q^2 /d^2 repulsive force
Ratio of the force F2 / F1 =( k * 2.625Q^2 /d^2 ) / ( k 3Q^2 /d^2 ) = 0.875
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