Two identical conducting spheres, fixed in place, attract eachother with an elec

Question

Two identical conducting spheres, fixed in place, attract eachother with an electrostatic force of .220 N when theircenter-to-center separation is 80cm. The spheres are then connectedby a thin conducting wire. When the wire is removed, the spheresrepel each other with an electrostatic force of 0.0350 N.

(a)What is the charge on each of the two spheres at the end?
(b) What is the amount of charge that was distributed between thespheres when the wire was connected?
(c)What was the charge on the original negative sphere
(d) What was the charge on the original positive sphere?

I am a stumped basically on the whole thing, thanks for anyhelp.

Explanation / Answer

Let the charge on each sphere be q and q ' Attractive force F = K qq ' / r ^ 2 where r = separation = 80 cm = 0.8 m            F= 0.22 N          K = coulomb'sconstant = 8.99 * 10 ^ 9 N m ^ 2 / C ^ 2 plug the values weget 0.22 = ( 8.99* 10 ^ 9 ) qq ' / (0.8 ) ^ 2 from this qq' = 0.01566 * 10 ^ -9   ----(1) After connected the wire : ------------------------- charge Q = ( q + q' ) / 2 force F ' = 0.035 N KQ^2 / r ^ 2 = 0.035 from this charge Q = [ 0.035 * r^ 2 / K ]                              = 0.1578 * 10 ^ -5                   q + q ' = 0.1578 * 10^5    ----( 2) from the equation ( q - q ' ) ^ 2 = (q + q' ) ^ 2 - 4qq' from this you find q - q ' value So, charges q = [ ( q  + q' ) + ( q - q ' ) ]/ 2                                                                 q' = [ ( q + q' ) - ( q - q ' ) ] / 2

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