 # If two identical conducting spheres are in contact, any exce lugreget9 2021-12-17 Answered
If two identical conducting spheres are in contact, any excess charge will be evenly distributed between the two. Three identical metal spheres are labeled A, B, and C. Initially, A has charge q, B has charge −q/2, and C is uncharged. a. What is the final charge on each sphere if C is touched to B, removed, and then touched to A? b. Starting again from the initial conditions, what is the charge on each sphere if C is touched to A, removed, and then touched to B?
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Intially, the charges of the spheres are

a. As is said in the problem, when spheres are brought in contact, any excess charge in them will be wqually split among them. Therefore, after C is touched to B we have
${q}_{B1}={q}_{C1}=\frac{12}{{q}_{B0}+{q}_{C0}}=-\frac{14}{q}$
Then when C is touched to A we have that
${q}_{A2}={q}_{C2}=\frac{12}{{q}_{A0}+{q}_{C1}}=\frac{38}{q}$
So the final charges of the sphesres A, B, and C are $\frac{38}{q},-\frac{14}{q},$ and $\frac{38}{q}$

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b. We start again from the initial conditions. When C is touched to A the new charges are
${q}_{A1}={q}_{C1}=\frac{12}{{q}_{A0}+{q}_{C0}}=\frac{12}{q}$
Then, if C is touched to B we have that
${q}_{B2}={q}_{C2}=\frac{12}{{q}_{B1}+{q}_{C1}}=0$
Therefore, the final charges of the spherse are $\frac{12}{q},0$ and 0.

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