You have four identical conducting spheres: A, B, C, and D. In each scenario, sphere A starts with a charge of +Q whereasB, C, and D start out with no net charge, and then the spheres are touched to each other and separated in the orderdescribed. Any spheres not in contact are held very far away. For each scenario, give the final charge of sphere D as a wholenumber fraction of Q. For example, if you decide that the final charge of sphere D is , enter 1 in the numerator and 7 inthe denominator.Remember! Before each scenario begins, spheres A, B, C, and D are reset to charges of +Q, 0, 0, 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 C touch and are separated, then C and D touch and are separated.Qp =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.

Answered: You have four identical conducting…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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 D as a whole
number fraction of Q. For example, if you decide that the final charge of sphere D is , 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, 0, 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 C touch and are separated, then C and D touch and are separated.
Qp =
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.

Expert Solution

Step 1

Given:-

When two spheres are touched each others it remains at same potential (V) and the charge rearrange to do the same and equal potential at each of them.

Potential of sphere surface A : $V_{1}$

$B : V_{2}$

Therefore,

$V_{A} = V_{B}$

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