Answer to Question #169791 in Electricity and Magnetism for Jannah

Question

Spheres A, B, and C have charges +8 C, +12 C, and -5 C, respectively. Spheres A and B touched each other and then separated. Sphere A then touched sphere C and then separated

a. What is the total charge on the three spheres before and after touching each other?

b. What is the final charge on each sphere assuming they are identical?

c. What is the final charge on each sphere assuming that rA = rB = 2rC?

Answer 1

• The total charge before is $8+12-5=15C$, the total charge after is also $15C$, as the charge is conserved.
• When the spheres A and B are touched, their total charge $8+12=20C$. As the spheres are identical, the charge is redistributed uniformly, i.e. $20/2=10C$ on each of the spheres. Then when the spheres A and C are touched, their total charge $10-5=5C$ is equally distributed, so $5/2=2.5C$ on each. Thus the charge after is $A: 2.5C, B:10C, C:2.5C$.
• The result of touching the spheres A and B is unchanged, as they are still identical. When the spheres A and C are touched, the charge is distributed in such way, that the potential on a surface is the same. The potential is proportional to $q/r$ and thus the charge is distributed as $q_A=2q_C$ and thus $q_A \approx 3.33C, q_C\approx 1.67C$. So the charges are $A: 3.33C, B:10C, C:1.67C$.