Question

Two charges of `-2 C` and `-3 C` are positioned on a line at points `4` and `-1`, respectively. What is the net force on a charge of `5 C` at `0`?

Answer 1

`115/8k_eC^2` to the negative direction.

Explanation:

Electrostatic force between two point charges can be calculated using Coulomb's law.
`F=k_e(q_1*q_2)/r^2`, where `k_e` is the Coulomb's constant(`k=8.99*10^9 Nm^2C^-2`), `q_1` and `q_2` are the charges and `r` is the distance.

Force between `-2C` (at the point 4) and `5C` (at the point 0) is
`F_1=k_e(2C*5C)/4^2=5/8k_eC^2`. The direction of `F_1` is positive, for the two point charges have opposite signs.

Force between `-3C` (at the point -1) and `5C` (at the point 0) is
`F_2=k_e(3C*5C)/1^2=15k_eC^2`. This is also an attractive force, so the direction is negative.

Therefore, the net force on a charge of `5C` at `0` is `15k_eC^2-5/8k_eC^2=115/8k_eC^2`, and its direction is negative.