You have tour Identical oonducting sphere: A. B. C. and D. In each scenario belo

Question

You have tour Identical oonducting sphere: 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 i touched to i 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 -Q7. enter in the numerator and "7" in the denominator Remember Before each see nano begins, spheres A B. C. and 0 are reset to charges of -Q. 0. Q. and 0 again. Soenano 1: A and B touch and are separated then A and C touch and are separated, then A and 0 touch and are separated Scenario Z. A and B touch and are separated, then B and 0 touch and; separated, then C and D touch and

Explanation / Answer

1)
A : -Q
B : 0
C : +Q
D : 0

after A and B are touched:
A : -Q/2
B : -Q/2
C : +Q
D : 0

after A and C are touched:
A : (-Q/2 + Q ) / 2 = Q/4
B : -Q/2
C : (+Q -Q/2)/2 = Q/4
D : 0

after A and D are touched:
A : +Q/8
B : -Q/2
C : +Q/4
D : Q/8
Answer: 1/8

2)
A : -Q
B : 0
C : +Q
D : 0

after A and B are touched:
A : -Q/2
B : -Q/2
C : +Q
D : 0

after B and D are touched:
A : -Q/2
B : -Q/4
C : +Q
D : -Q/4

after C and D are touched:
A : -Q/2
B : -Q/4
C : (+Q -Q/4)/2 = 3*Q/8
D : (-Q/4 + Q ) /2 = 3*Q/8
Answer: -1/2

3)
A : -Q
B : 0
C : +Q
D : 0

after A and D are touched:
A : -Q/2
B : 0
C : +Q
D : -Q/2

after C and D are touched:
A : -Q/2
B : 0
C : +Q/4
D : +Q/4

after A and D are touched:
A : -(Q/2 + Q/4 )/2 = 3*Q/8
B : 0
C : +Q/4
D : (+Q/4 + Q/2)/2 = 3*Q/8

after A and B are touched:
A : 3*Q/16
B : 3*Q/16
C : +Q/4
D : 3*Q/8
Answer: 3/16

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