Electric charge, conservation, Coulomb's law, superposition

Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (Radii of A and B are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as :

Two point charges A and B, having charges \(+Q\) and \(-Q\) respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes :

Suppose the charge of a proton and an electron differ slightly. One of them is \(-e\), the other is \((e+\Delta e)\). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then \(\Delta e\) is of the order of [Given mass of hydrogen \(m_h = 1.67\times10^{-27}\) kg]

Two identical charged spheres suspended from a common point by two massless strings of lengths \(l\), are initially at a distance d (d << \(l\)) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity \(v\). Then \(v\) varies as a function of the distance \(x\) between the spheres, as :