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 -0.9155 N when separated by 50 cm, center-to-center. 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 0.0756 N. what were the initial charges on the spheres? since one is negative and you cannot tell which is positive or negative, there are two solutions. Take the absolute value of the charges and enter the smaller value here.

enter the larger value here.

Explanation / Answer

Force between the spheres :

F = k*q1*q2/r^2 = 0.9155

So, 9*10^9*q1*q2/(0.5)^2 = 0.9155

So, q1*q2 = 2.54*10^-11 N -------- (1)

When the wire is connected, the charges distribute equally,

So, charges on each : q = (q1-q2)/2 <------ taking charge q1 > q2

Now, the force, F' = 9*10^9*q^2/0.5^2 = 0.0756

So, q = 1.45*10^-6 C = (q1 - q2)/2 ---------- (2)

Solving the two equations (1) and (2): we get :

q1 = 6.7*10^-6 , q2 = 3.8*10^-6 C <------- initital charges

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