Two identical charges interact with each other at a distance of 13cm with a force

Two identical charges interact with each other at a distance of 13cm with a force of 0.25mN. Find the number of excess electrons on charges.

r = 13 cm = 0.13 m.

q1 = q2.

k = 9 * 10 ^ 9 N * m2 / Cl2.

F = 0.25 mN = 0.25 * 10 ^ -3 N.

q1 = 1.6 * 10 ^ -19 Cl.

n -?

To find the number of excess electrons n, it is necessary to divide the charge q by the charge of one electron q1: n = q / q1.

The force of interaction between electric charges F is determined by Coulomb’s law.

The force of interaction is directly proportional to the magnitude of these charges q1 and q2 and is inversely proportional to the square of the distance between them r: F = k * q1 * q2 / r ^ 2 = k * q ^ 2 / r ^ 2.

q = √ (F * r ^ 2 / k).

q = √ (0.25 * 10 ^ -3 H * (0.13 m) ^ 2/9 * 10 ^ 9 N * m2 / Cl2) = 21.65 * 10 ^ -9 Cl.

n = 21.65 * 10 ^ -9 C / 1.6 * 10 ^ -19 C = 13.53 * 10 ^ 10.

Answer: each charge contains n = 13.53 * 10 ^ 10 excess electrons.