We have three identical metallic spheres A, B, C. Initially sphere A is charged with charge Q, while B and C are neutral. First, sphere A is brought into contact with sphere B and then separated from it. After that, sphere A is brought into contact with sphere C and then separated from it. Finally, sphere A is brought into contact with sphere B again, and then separated from it
What is final charge of sphere A?

Question

16-01-2020
Physics

contestada

We have three identical metallic spheres A, B, C. Initially sphere A is charged with charge Q, while B and C are neutral. First, sphere A is brought into contact with sphere B and then separated from it. After that, sphere A is brought into contact with sphere C and then separated from it. Finally, sphere A is brought into contact with sphere B again, and then separated from it
What is final charge of sphere A?

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creamydhaka creamydhaka · Answer 1 · 2020-01-16T07:10:29+01:00

Answer:

[tex]Q_A=\frac{3}{8} Q[/tex]

Explanation:

Given that sphere A has Q charge on it.

Spheres B & C are neutral.

After the sphere A & B are brought in contact, the charges flow till both the metallic spheres attain the same quantity of charge.

So,

Charge on the each of the metallic spheres A & B after initially brought in contact:

[tex]Q_A=Q_B=\frac{Q}{2}[/tex]

Now when sphere A is brought in contact with sphere C then the charges on A & C will be:

[tex]Q_A=Q_C=\frac{Q}{4}[/tex]

Now when again sphere A is brought in contact with sphere B then the charges will be as:

[tex]Q_A=Q_B=(\frac{Q}{4} +\frac{Q}{2} )\div 2[/tex]

[tex]Q_A=Q_B=\frac{3}{8} Q[/tex]

jtellezd jtellezd · Answer 2 · 2021-09-04T18:59:47+02:00

Solution: The final charge on sphere A is Q/4 ( in units of electric charge)

The Energy conservation principle implies that when spheres A and B are in contact the original charge on sphere A will redistribute between the two spheres, as the spheres are identical, the charge will redistribute an equal amount over the two spheres, or sphere A after the separation will keep half of the charge (Q/2) and sphere B ( Q/2).

Now sphere A has Q/2 as charge; we place sphere C and sphere A in contact, and again the charge will redistribute, in that case as charge in sphere A is Q/2 and again the spheres are identical, after the separation spheres A will keep Q/4.