You have four identical conducting spheres: A, B, C, and D. In each scenario bel

Question

You have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with a charge of Q, while B, C, and D start out with no net charge, and then the spheres are touched to each other and separated in the order described. Any spheres not in contact are held very far away. For each scenario, give the final charge of sphere D as a whole number fraction of Q. For example, if you decide that the final charge of sphere D is Q/7, enter "1" in the numerator and "7" in the denominator. Remember! Before each scenario begins, spheres A, B, C, and D are reset to charges of Q, 0, 0, and 0 again.

2)

Scenario 2: A and B touch and are separated, then B and C touch and are separated, then C and D touch and are separated.

3)

A and D touch and are seperated, then D and C touch and are seperated, then D and A touch and are seperated, then A and B touch and are seperated

Explanation / Answer

well when the spheres are touched to each other , their potential becomes equal,
so in the first step,
let the charge flowed be q
(-Q+q)k/r= -qk/r
or q=Q/2
now charge on a is -Q/2 and on D is -Q/2
now second step,
let the charge flowed be q
(Q-q)k/r= (-Q/2+q)k/r
or q=3Q/4
so charge on D is Q/4 and on C is Q/4
now for the third step,
let the charge flowed be q
so,
(-Q/2+q)k/r=(Q/4-q)k/r
or q= 3Q/8
so charge on A is -Q/8 and so is the charge on D
now the final step,
let the charge flowed be q,so
(-Q/8+q)k/r=-qk/r
or q=Q/16
so the final charge on B is -Q/16
hope this is correct and u would appreciate me by awarding me karma points

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