You have three identical metal spheres that have different initial net charges.

Question

You have three identical metal spheres that have different initial net charges. Sphere A has a net charge of +3Q; sphere B has a net charge of -2Q; and sphere C has a net charge of +6Q. You first touch sphere B to sphere A, and then separate them; you then touch sphere B to sphere C, and then separate them; and finally you touch sphere A to sphere C, and then separate them.

(a) Assuming no charge is transferred to you, what is the total combined charge on the three spheres at the end of the process?
Q
(b) What is the charge on sphere A at the end of the process?
Q
(c) What is the charge on sphere B at the end of the process?
Q

Explanation / Answer

1)First step B to A

B -2Q

A +3Q

then charge on each sphere is (+3Q-2Q)/2 = +Q/2

B +Q/2

A +Q/2

2)Then B to C

B +Q/2

C +6Q

Charge on each sphere after touching is (6Q+Q/2)/2 = +3.25 Q

B +3.25Q

C +3.25Q

3)Then A to C

A +Q/2

C +3.25Q

Charge on each sphere after touching is (3.25Q+0.5Q)/2 = +1.875 Q

A  +1.875 Q

C +1.875 Q

Final charges on spheres are

A +1.875Q

B +3.25Q

C +1.875Q

You can see that the net charge is conserved, the total charge is nothing but +7 Q

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