You have four identical conducting spheres: A,B,C, and D. In each scenario below

Question

You have four identical conducting spheres: A,B,C, and D. In each scenario below, sphere A starts with a charge of -Q, sephere C starts wiht a charge of +Q, and sepheres B and D start out neutral. Then the sepheres are touched to each other and seperated in the order described. Any spheres not in contanct are held very far away. For each scenario, give the final charge of sphere B as a whole number fraction of Q. For example, if you decide that the final charge of sephere B is - Q/7, enter "1" in the numerator and "7" in the denominator.

Explanation / Answer

Scenario 1:

As sphere B only touches with A having charge -Q, charge will be equally distributed.

Suppose now charge of A and B are Q1 and Q2 respectively, then

Q1 = Q2

and, Q1 + Q2 = -Q (conservation of charge)

so, Q1 = Q2 = -Q/2

Charge on Sphere B is

Numerator : -1

Denominator : 2

Scenario 2:

After A touched with B,

charge on B is -Q/2.

Now B is touched with D which is nuteral.

Same corservation of charge scenario,

Now charge on B is -Q/4

Numerator : -1

Denominator : 4

Scenario 3 :

After A touched with D,

charge on both spheres is -Q/2.

Now D touches with C,

now charge on D is (-Q/2 + Q)/2 = Q/4

Now, D touches with A again,

charge on A now is (Q/4 -Q/2)/2 = -Q/8

Now A touches with B,

so charge on B is -Q/16.

Numerator : -1

Denominator : 16

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