Question

# Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.5574...

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of -0.5574 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 0.0325 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.

Let q1 and q2 are the initial charges on the spheres.

F = k*q1*q2/d^2

-0.5574 = 9*10^9*q1*q2/0.5^2

==> q1*q2 = -0.5575*0.5^2/(9*10^9)

q1*q2 = -1.548*10^-11 ---(1)

when they are connected q1' = q2' = (q1+q2)/2

F' = k*q1'*q2'/d^2

0.0325 = 9*10^9*( (q1+q2)/2)^2/0.5^2

((q1+q2)/2)^2 = 0.0325*0.5^2/(9*10^9)

q1+q2 = 2*sqrt(0.0325*0.5^2/(9*10^9) )

q1 + q2 = 1.9*10^-6 ---(2)

on solving the two equations

q1 = -3.1*10^-6 C and q2 = 5*10^-6 C

or

q1 = 5*10^-6 C and q2 = -3.1*10^-6 C