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 44.2 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 0.0529 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge in coulombs on one of them and (b) the positive charge in coulombs on the other?

Explanation / Answer

q1 is positive, -q2 is negative when joined the charges on each are (q1-q2)/2 , (q1-q2)/2 F_initial = Kq1q2/r^2 0.127 = 8.98*10^9*q1q2/(0.442)^2 ..............> equation 1 F_final = k [(q1-q2)^2]/r^2 F_initial/F_final = q1q2/[(q1-q2)^2] = 0.127/0.0529 ........> equation 2 there are two unknowns (q1, q2) and there are two equations. so by solving equations 1 and 2 we get q1 and q2

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