At what distance do you need to place two charges 5 • 10-9 and 6 • 10-9 C

At what distance do you need to place two charges 5 • 10-9 and 6 • 10-9 C, so that they repel with a force of 12 • 10-4 N?

q1 = 5 * 10-9 Cl.

q2 = 6 * 10-9 Cl.

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

F = 12 * 10-4 N.

r -?

According to Coulomb’s law, the force of interaction between charges F 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 / r2.

k – coefficient of proportionality, the value of which is k = 9 * 10 ^ 9 N * m2 / Cl2.

r2 = k * q1 * q ^ 2 / F.

r = √ (k * q1 * q ^ 2 / F).

r = √ (9 * 10 ^ 9 N * m2 / Cl2 * 5 * 10-9 Cl * 6 * 10-9 Cl / 12 * 10-4 N) = 0.15 m.

Since the charges are repelled, it means they have the same signs.

Answer: electric charges are located at a distance r = 0.15 m from each other.