you have four identical conducting sphere You have four identical conducting sph

Question

you have four identical conducting sphere 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

Explanation / Answer

(A)

In first step, Charge on A and B = Q+0/2 =Q/2

In second step, Charge on A and C= [Q/2 +0] / 2 = Q/4

In third step, charge Charge on A and D = [Q/4+0]/2 = Q/8

So QD = Q/8

(B)

In first step, Charge on A and B = Q+0/2 =Q/2

In second step, Charge on B and C= [Q/2 +0] / 2 = Q/4

In third step, charge Charge on C and D = [Q/4+0]/2 = Q/8

So QD = Q/8

(C)

In first step, Charge on A and D = Q+0/2 =Q/2

In second step, Charge on D and C= [Q/2 +0] / 2 = Q/4

In third step, charge Charge on D and A = [Q/4+Q/2]/2 = 3Q/8

In third step, charge Charge on A and B = [3Q/8+0]/2 = 3Q/16

So QD = 3Q/8

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