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 -0.4085 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 0.2719 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. T

Take the absolute value of the charges and enter the smaller value here.

Enter the larger value here.

Explanation / Answer

LEt initial charges in sphere 1 = q1 and sphere 2 = q2

Force, F = kq1q2/r2 = 0.4085 (attractive since the sign is negative)

q1q2 = (0.4085*r2)/k = 1.134e-11 -------- equation 1

After wire is connected charge distrbute equally between the two as they are identical

let the new charge be Q

kQ^2/r^2 = 0.2719

Q = sqrt(0.2719*r^2)/k = 2.75e-6

By conservation of charge

q1 + (-q2) = 2.75e-6

q1 = 2.75e-6 + q2

from equation 1 we have

q1 = 2.75e-6 + 1.134e-11/q1

let q1 = x

x^2 - 2.75e-6 x - 1.134e-11 = 0

x = 5.01e-6 , -2.26e-6

Therefore

q1 = 5.01e-6 C

q2 = -2.26e-6 C

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