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 -1.0799 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 0.1298 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.

please show work

Explanation / Answer

Let the initial charges be q1 & q2

Let final charge be q on each

Initially:

k*q1*q2/0.5^2 = -1.0799

=> q1*q2 = - 3*10^-11

Finally:

kq^2/0.5^2 = 0.1298

=> q = Sqrt(3.6*10^-12)

=> q = 1.9*10^-6

Also,

q1 + q2 = q + q

=> q1 + q2 = 3.8 * 10^-6 ......................(1)

Now,

(q1 - q2)^2 = (q1 + q2)^2 - 4*q1*q2

=> q1 - q2 = Sqrt[ (3.8*10^-6)^2 - 4*(-3*10^-11)]

=> q1 - q2 = Sqrt(1.34*10^-10)

=> q1 - q2 = 1.16*10^-5 .................(2)

Add (1) & (2)

=>> 2q1 = 1.54*10^-5

=> q1 = 7.7 micro C

& q2 = - 3.9 micro C

Absolute values are 7.7 & 3.9 micro C

And smaller one is 3.9 micro C

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