sapling learming Map You have four identical conducting sphe

sapling learming Map You have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with a charge of -Q, sphere C starts out with a charge of+Q, and spheres B and D start out neutral. 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 A as a whole number fraction For example, if you decide that the final charge of sphere A is-d/7, enter \"-1\" in the numerator an of Q. d \"7\" in the denominator Before each scenario begins, spheres A, B, C, and D are reset to charges of-Q, 0, +Q, and O again. Scenario 1: A and B touch and are separated, then A and C touch and are separated, then A and D touch and are separated enario 2: A and B touch and are separated, then B and D touch and are separated, then C and D touch and are separated Scenario 3: A and D touch and are separated, then D and C touch and are separated, then D and A touch and are separated, then A and B touch and are separated x Q O Previous Give Up & View Solution e Check Answer 0 Next Exit

Solution

· All the given intial charges of given identical spheres A,B,C and D are -Q,0,0 and +Q respectively. then based on charge conservation principle,

Scenario 1

in this if A and B are touched each other and separated then the charge on A becomes -Q/2 and B becomes -Q/2

similarly later if A and C are touched and separated then charge on A becomes Q/4 and C becomes Q/4

later if A and D are touched and separated then charge on A finally becomes Q/8 and D becomes Q/8

Finally the charge on A is 1/8

Scenario 2

if A and B are touched each other and separated then the charge on A becomes -Q/2 and B becomes -Q/2

After that B and D are touched each other and separated and C and D are touched and separated. hence there is no change in the charge on A.

Finally the charge on A is -1/2

Scenario 3

in this first A and D are touched each other and separated and Charge on A becomes- Q/2 and charge on D becomes -Q/2

later D and C are touched and separated and the charge on D becomes Q/4 and the charge on C becomes Q/4

later D and A are touched each other and separated and the charge on A becomes -Q/4 and the charge on D becomes -Q/4

at last A and B are touched each other and separated and the charge on A becomes -Q/8 and the charge on B becomes -Q/8

Hence finally the charge on A is -1/8