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 other 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 -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. Q_A = times Q 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. Q_A = times 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. Q_A = times Q

Explanation / Answer

whenever two spheres are touched, total charge on each of them is equally distributed.

S1:

A and B touched

total charge on A and B = -Q, So

Charge on A = Charge on B = -Q/2

Now A and C touched,

total charge on A and C = -Q/2 + Q = Q/2

Charge on A = Charge on C = Q/4

Now A and D touched

total charge on A and D = Q/4 + 0 = Q/4

Charge on A = Charge on C = Q/8

Final Charge on A = Q/8 = (1/8)*Q

S2:

A and B touched

total charge on A and B = -Q, So

Charge on A = Charge on B = -Q/2

Now B and D touched,

total charge on B and D = -Q/2 + 0 = -Q/2

Charge on B = Charge on D = -Q/4

Now C and D touched

total charge on C and D = Q + (-Q/4) = 3Q/4

Charge on C = Charge on D = 3Q/8

Final Charge on A = -Q/2 = (-1/2)*Q

S3:

A and D touched

total charge on A and D = -Q, So

Charge on A = Charge on D = -Q/2

Now D and C touched,

total charge on D and C = -Q/2 + Q = Q/2

Charge on D = Charge on C = Q/4

Now D and A touched

total charge on D and A = Q/4 - Q/2 = -Q/4

Charge on D = Charge on A = -Q/8

Now A and B touched

total charge on A and B = -Q/8 + 0 = -Q/8

Charge on A = Charge on B = -Q/16

Final Charge on A = -Q/16 = (-1/16)*Q

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.