Question

Two electrically-charges spheres are suspended from insulated threads a certain distance from each other. There is a certain amount of electrostatic force between them. Describe specifically (not just increase or decrease) what happens to this force in each of the scenarios below (1 pt. ea.):
The charge on one sphere is reduced by half
The charge on both spheres is doubled
The distance between the spheres is increased by a factor of three
The distance between the sphere is decreased to one-fourth
The charge of each sphere is doubled and the distance between them is doubled

Answer 1

@Michele_Laino

Answer 2

let's suppose to have 2 charges, namely Q_1 and Q_2, separated by a distance d. Then the interaction force F (its magnitude) is equal to:
\[F = k\frac{{{Q_1}{Q_2}}}{{{d^2}}}\]

Answer 3

now, we have:
scenario #1
let's suppose that the new charge is Q_1/2, then the new force is:
\[{F_1} = k\frac{{\left( {{Q_1}/2} \right){Q_2}}}{{{d^2}}} = k\frac{{{Q_1}{Q_2}}}{{2{d^2}}} = \frac{F}{2}\]

Answer 4

please do the same with other scenarios