lugreget9

2021-12-17

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?

Bertha Jordan

Beginner2021-12-18Added 37 answers

Intially, the charges of the spheres are

${q}_{A0}=q,\text{}{q}_{B0}=-\frac{12}{q},\text{}{q}_{C0}=0$

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 $\frac{38}{q}$

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

Then when C is touched to A we have that

So the final charges of the sphesres A, B, and C are

Philip Williams

Beginner2021-12-19Added 39 answers

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.

Then, if C is touched to B we have that

Therefore, the final charges of the spherse are

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