Question

Two identical conducting spheres, fixed in place, attract each
other with an electrostatic force of -0.2848 *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 0.0608
*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

Answer #1

F1 = -kq1q2/r^2 = 0.0911 N, and

F2 = kq3^2/r^2 = 0.0297 N, where 2q3 = q1+q2 due to conservation of
charge.

Solving for q3,

q3 = sqrt(0.0297r^2/k) = 7.8658E-7 C

Then solving for q1 we have

F1 = -kq1(2*7.8658E-7-q1)/r^2 = 0.0911 which yields a
quadratic

-q1^2 + 2*7.8658E-7q1 + 0.0911r^2/k = 0 resulting in

q1 = 2.37293E-6 C and q2 = -7.99772E-7 C, which sum to 2*7.8658E-7
C

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