Two identical conducting spheres, fixed in place, attract each other with an ele

Question

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.127 N when their center-to-center separation is 67.2 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0355 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude.)

Explanation / Answer

suppose negatively charged has charge magnitude of q1 and other positive charges q2.

so attraction electrostatic force = kq1q2 / d^2 = 0.127

(9 x 10^9 x q1 x q2 ) / (0.672^2) = 0.127

q1q2 = 6.37 x 10^-12

when they are connected by wire then they will acquire same charge lets say q

using charge conservation,

(-q1) + q2 = q + q

q = (q2 - q1)/2

now repeling force, kqq / d^2 = 0.0355

(9 x 10^9 x (q1 - q2)^2 / 4) / 0.672^2 = 0.0355

q2 - q1 = 2.67 x 10^-6

q2 = q1 + 7.12e-6

putting in previous equation,

q1 ( q1 + 7.12e-6) = 6.37e-12

q1^2 + 7.12e-6q1 - 6.37e-12 = 0

q1 = 8.04 x 10^-7

so q2 = 8.04e-7 + 7.12e-6 = 7.92 x 10^-6

-ve charge = -8.04 x 10^-7 C

+ve charge = 7.93 x 10^-6 C

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