Answer to Question #170913 in Electricity and Magnetism for Cass

Question

One charge of 2.0C is 1.5m away from a -3.0e charge. Determine the force they exert from each other.

Answer 1

The task is not accurately stated, it is not clear, if the second charge is $-3.0 e$ (e is the charge of electron) or it is $-3.0\,\mathrm{C}.$ So we'll discuss all cases.

1) Let $q_1$ be $2.0\,\mathrm{C}$ and $q_2$ be $-3.0\,\mathrm{C}$ . According to the Coulomb's law, the force between two charges is

$F = \dfrac{kq_1q_2}{r^2},$ where r is the distance between two charges.

$F = \dfrac{9\cdot10^9\cdot 2.0\cdot3.0}{1.5^2} = 2.4\cdot10^{10}\,\mathrm{N}.$ Due to the difference in signs of charges, the charges will attract to each other. And due to the quite big charges the force is enormous.

2) Let $q_1$ be $2.0\,\mathrm{C}$ and $q_2$ be $-3.0 e$. According to the Coulomb's law, the force between two charges is

$F = \dfrac{kq_1q_2}{r^2},$ where r is the distance between two charges.

$F = \dfrac{9\cdot10^9\cdot 2.0\cdot3.0\cdot 1.6\cdot10^{-19}}{1.5^2} =4\cdot10^{-9}\,\mathrm{N}.$ Due to the difference in signs of charges, the charges will attract to each other.

In both cases the force is attractive and according to the third Newton's law the moduli of forces exerted by the charges are equal to each other, but the directions of forces are opposite.