Question

If two charged balloons are 20cm apart and they feel a force of electrical repulsion of 50N, what would the force of electrical repulsion become if the balloons were moved apart to a distance of 100cm?

Answer 1

According to Coulomb's law, the force of electrical repulsion is

$F = k_e\dfrac{q_1q_2}{r^2}$ . Therefore, if we increase the distance 5 times, the force decreases $5^2=25$ times. We may write it as

$\dfrac{F_2}{F_1} = \dfrac{k_e\dfrac{q_1q_2}{r_2^2}}{k_e\dfrac{q_1q_2}{r_1^2}} = \dfrac{r_1^2}{r_2^2} = \left(\dfrac{r_1}{r_2} \right)^2 = \left(\dfrac{20}{100} \right)^2 = \dfrac{1}{25}.$

So $F_2 = F_1/25= 50\,\mathrm{N}/25 = 2\,\mathrm{N}.$