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, 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 C as a whole number fraction of Q For example, if you decide that the final charge of sphere C 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, +Q, and 0 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 Scenario 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

Explanation / Answer

Given

QA = -Q

QB = 0

QC = +Q

QD = 0

Solution

1)

A and B are touched the share charges equally

New charge on A and B will be

(-Q + 0)/2 = -Q/2

Now A is touched with C

The total charge in this collection is

(-Q/2) +Q = +Q/2

This charge will be equally shared by A and C so charge on A and C is

(+Q/2)/2 = +Q/4

After this sphere C is not disturbed

So charge on sphere C is

Qc = (1/4) x Q

2)

A and B are touched the share charges equally

New charge on A and B will be

(-Q + 0)/2 = -Q/2

Now B and D are touched

Total charge of these two spheres will be

-Q/2 + 0 = -Q/2

This will be equally shared by B and D so their new charge is

(-Q/2) / 2 = -Q/4

Now spheres C and D touch. Their total charge

+Q + (-Q/4) = +3Q/4

it will be equally charred by both C and D so their new charge is

(+3Q/4) / 2 = +3Q/8

so the charge on sphere C is

Qc = (3/8) x Q

3)

A and D are touched the share charges equally

New charge on A and D will be

(-Q + 0)/2 = -Q/2

Now D and C are touched

Their total charge is

(-Q/2) + Q = +Q/2

This charge will be shared by D and C equally

So their new charge will be

(+Q/2)/2 = +Q/4

after this the sphere C is not disturbed

So

Qc = (1/4) x Q

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