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 -0.3323 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 0.3798 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

F1 = -kq1q2/r2 = -0.3323 N, and

F2 = kq32/r2 = 0.3798 N,

where 2q3 = q1+q2 due to conservation of charge.

Solving for q3,

q3 = sqrt(0.3798r2/k) = 3.2480 x 10-6 C

Then solving for q1 we have

F1 = -kq1(2*3.2480 x 10-6-q1)/r2 = -0.3323 which yields a quadratic

-q12 + 0.000006496q1 - 0.3323r2/k = 0 resulting in

q1 = 0.00000209954 (Bigger Value)

q2 = 0.00000439645 (Smaller Value)

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