Question

You have four identical conducting spheres: A, B, C, and D. In each scenario, sphere A starts with a charge of +?+Q whereas 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 A as a whole number fraction of ?.Q. For example, if you decide that the final charge of sphere A is ?7,Q7, enter 11 in the numerator and 77 in the denominator.

Remember! Before each scenario begins, spheres A, B, C, and D are reset to charges of +?,+Q, 0,0, 0,0, and 00 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.

?A=QA=

×?×Q

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.

?A=QA=

×?×Q

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.

?A=QA=

×?

Answer 1

Given four conducting  spheres A,B,C,D

Off these sphere A is charged to a magnitude Q at the beginning of each scenario .

Spheres B,C,D are charged to zero at the beginning of each scenario

SCENARIO 1 :

First A and B are touched that implies they share the charge of sphere A equally

that is initial total charge = Q

after dividing equally , A = Q/2 , B = Q /2

Then A and C are touch and separated , they share the their total charge equally

that is  initial total charge = Q/2

after dividing equally , A= Q /4 , C = Q/4

Then A and D are touch and separated , they share the their total charge equally

that is  initial total charge = Q/4

after dividing equally , A= Q /8 , D = Q/8

Final charge of A = Q/8 = Q * (1/8)

It is already in the whole number fraction .

SCENARIO 2 :

First A and B are touched that implies they share the charge of sphere A equally

that is initial total charge = Q

after dividing equally , A = Q/2 , B = Q /2

Then B and C are touch and separated , they share the their total charge equally

that is  initial total charge ( only B has charge initially)= Q/2

after dividing equally , B= Q /4 , C = Q/4

Then C and D are touch and separated , they share the their total charge equally

that is  initial total charge( only C had charge initially ) = Q/4

after dividing equally , C= Q /8 , D= Q/8

Final charge of A = Q/2 = Q*(1/2)

It is already written in whole number fraction .

SCENARIO 3 :

First A and D are touched that implies they share the charge of sphere A equally

that is initial total charge = Q

after dividing equally , A = Q/2 , D= Q /2

Then D and C are touch and separated , they share the their total charge equally

that is  initial total charge ( only D has charge initially)= Q/2

after dividing equally , D= Q /4 , C = Q/4

Then A and D are touch and separated , they share the their total charge equally

that is  initial total charge( both A and D had charge initially ) = Q/4 + Q/2 = 3Q/4

after dividing equally , A= 3Q /8 , D= 3Q/8

Then A and B are touch and separated , they share the their total charge equally

that is  initial total charge(only A had charge   initially ) = 3Q/8

after dividing equally , A= 3Q /16 , B= 3Q/16

Final charge of A = 3Q/16= Q*(3/16)

But as instructed in the question that is if i get 7Q , i need to write it as (11/77) Q

so in that case

SCENARIO 1 :  We got Q/8 , we can write it as (2/16) Q

SCENARIO 2 :  We got Q/2 , we can write it as (4/8) Q

SCENARIO 3 : We got 3Q/16 , we can write it as (6/32) Q