Question

If one of the charges is doubled in magnitude while maintaining the same separation between the charges, what is the new magnitude of the force between them?

Answer 1

Magnitude of force doubles.

Explanation:

Force between two charges is given by

              $F=k\frac{q_1q_2}{r^2}$

where q₁ and q₂ are charges and r is the distance between them.

Here one charge is doubled with keeping all others same.

            q₁ = 2 q₁

We have

               $F_1=k\frac{q_1q_2}{r^2}\\\\F_2=k\frac{2q_1q_2}{r^2}\\\\\frac{F_1}{F_2}=\frac{k\frac{q_1q_2}{r^2}}{k\frac{2q_1q_2}{r^2}}\\\\\frac{F_1}{F_2}=\frac{1}{2}\\\\F_2=2F_1$

Magnitude of force doubles.