any help would be greatly appreciated!! Two identical conducting spheres, fixed

Question

any help would be greatly appreciated!!

Two identical conducting spheres, fixed in place, attract eachother with an electrostatic force of 0.116 N when theircenter-to-center separation is 58.9 cm. The spheres are thenconnected by a thin conducting wire. When the wire is removed, thespheres repel each other with an electrostatic force of 0.0479 N.Of the initial charges on the spheres, with a positive net charge,what was (a) the negative charge in coulombs onone of them and (b) the positive charge incoulombs on the other?

Explanation / Answer

Attractive force F = 0.116 N      Kqq' /r^ 2 = 0.116 N where q , q ' = charges of two spheresrespectively             qq ' = 0.116 * r ^ 2 / K where r = separation = 58.9 cm = 0.589 m           K =coulomb's constant = 8.99 * 10 ^ 9 N m ^ 2 / C ^ 2 plug the values   q q ' = 4.4764 * 10 ^ -12 -------------( 1) Charge on each sphere after connecting through a wire Q= ( q + q ' ) / 2 So, repulsive force F ' = 0.0479 N       K Q ^ 2 / r ^ 2 = 0.0479N from this   Q = r [ 0.0479 / K ]                     =r * 0.2308 * 10 ^ -5                   = 0.589 * 0.2308* 10 ^ -5                    = 0.13595 * 10 ^-5             q + q ' = 2 * 0.13595 * 10 ^ -5               = 0.2719 * 10 ^ -5    --------------( 2) ( q- q ' ) ^ 2= ( q + q ' ) ^ 2 - 4qq ' from this we find q - q ' value So, charge on one sphere q = [ ( q + q ' ) + ( q - q ' )] / 2 charge on second sphere q ' = [ ( q + q ' ) - ( q -q ' ) ] / 2 So, charge on one sphere q = [ ( q + q

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