Question

Suppose you have three identical metal spheres, AA, BB, and CC. Initially sphere AA carries a charge qq and the others are uncharged. Sphere AA is brought in contact with sphere BB, and then the two are separated. Spheres CC and BB are then brought in contact and separated. Finally spheres AA and CC are brought in contact and then separated. What is the final charge on the sphere B, in terms of q?
a. 3/8q

b. 1/4q

c. 3/4q

d. q

e. 5/8q

f. 1/3q

g.1/2q

h. 0

Answer 1

Complete Question

Suppose you have three identical metal spheres, A, B, and C. Initially sphere A carries a charge q and the others are uncharged. Sphere A is brought in contact with sphere B, and then the two are separated. Spheres CC and BB are then brought in contact and separated. Finally spheres AA and CC are brought in contact and then separated. What is the final charge on the sphere B, in terms of q?

a. 3/8q

b. 1/4q

c. 3/4q

d. q

e. 5/8q

f. 1/3q

g.1/2q

h. 0

Answer:

   The correct option is b

Explanation:

From the question we are told that

          The charge carried by A is  q C

           The charge carried by B is 0 C

            The charge carried by C is 0 C

When A and B are brought close and then separated the charge carried by  A and B is mathematically evaluated as

                 $\frac{ 0 + q}{2} = \frac{q}{2}$

When C and B are brought close and then separated the charge carried by  C and B  is mathematically evaluated as    

                    $\frac{0 + \frac{q}{2} }{2} = \frac{q}{4}$

When C and A are brought close and then separated the charge carried by  C and A  is mathematically evaluated as  

                       $\frac{\frac{q}{4} + \frac{q}{2} }{2} = \frac{3q}{8}$

Looking at these calculation we can see that the charge carried by B is

        $\frac{q}{4} C$