There are two identical, positively charged conducting spheres fixed in space. T

Question

There are two identical, positively charged conducting spheres fixed in space. The spheres are 31.6 cm apart (center to center) and repel each other with an electrostatic force of F1 = 0.0795 N. Then, a thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed the spheres still repel but with a force of F2 = 0.100 N. Using this information, find the initial charge on each sphere, q1 and q2 if initially q1. Please answer with numerical answers and explanation. Thank you.

Explanation / Answer

After the spheres are connected, the charges redistribute so there is the same (positive) charges, Q, on each sphere

F= kq1q2/r^2

0.1 = 9*10^9 * Q * Q /(0.316^2)

Q = sqrt(1.11*10^(-12)) = 1.053*10^(-6) C

now total charge on both sphere = 2*Q = 2.106*10^(-6) C

so q1 + q2 = 2.106*10^(-6) C

now before seperation

0.0795 = 9*10^9 * q1 * q2 /(0.316^2)

q1 * q2 = 8.82*10^(-13) C^2

q2 = 8.82*10^(-13) / q1

q1 + 8.82*10^(-13) / q1 = 2.106*10^(-6)

q1^2 - 2.106*10^(-6)*q1 + 0.882*10^(-12) = 0

q1 = 1.53*10^(-6) C

q2 = 0.576*10^(-6) C

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