Question

Chapter 18, Problem 05 Your answer is partially correct. Try again. Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +6q. Sphere B carries a charge of -q. Sphere C carries no net charge. Spheres A and B are touched together and then separated. Sphere C is then touched to sphere A and separated from it. Lastly, sphere C is touched to sphere B and separated from it. (a) What is the ratio of the final charge on sphere C to q? What is the ratio of the final total charge on the three spheres to q (b) before they are allowed to touch each other and (c) after they have touched? (a) Numbe-1 (b) Number (c) Number-1 UnitsT No units Un No units UnitsT No units

Answer 1

Initial charge on (A) = +6 q
Initial charge on (B) = -q
Initial charge on (C) = 0
Now A and B are touched therefore after separation
charge on A = +2.5 q
Charge on B = +2.5 q
Now sphere A is touched with C , then charge after separation will be
Charge on (A) = +1.25 q
Charge on (C) = +1.25 q
Lastly sphere C is touched with B , then charge after separation will be
Charge on C = 1.875 q
Charge on B = 1.875 q
Hence the final charge on A , B and C would be
Charge on (A) = +1.25 q
Charge on B = 1.875 q
Charge on C = 1.875 q
(a)
Ratio of final charge on C to q
$\frac{1.875 *q}{q} = 1.875$
hence answer would be 1.875
(b)
total charge on three sphere = 6q -q +0 = 5*q
hence the ratio of total charge on sphere to q
$\frac{5 *q}{q} = 5$
Hence the answer would be 5
(c)
total charge on three sphere = (1.25+1.875+1.875)q = 5*q
hence the ratio of total charge on sphere to q
$\frac{5 *q}{q} = 5$
Hence the answer would be 5