Determine the charges of two equally charged bodies interacting in a vacuum with a force of 5.8 ∙ 10

Determine the charges of two equally charged bodies interacting in a vacuum with a force of 5.8 ∙ 10 ^ –5 N at a distance of 100 cm.

Data: the considered bodies interacting in a vacuum have the same charge (q1 = q2 = q); F (force of interaction) = 5.8 * 10-5 N; r (distance between the considered bodies) = 100 cm (in SI r = 1 m).

Reference values: k (proportionality coefficient) = 9 * 10 ^ 9 N * m2 / Cl2.

We express the charges of the bodies under consideration from the formula: F = k * q1 * q2 / r ^ 2 = k * q ^ 2 / r ^ 2, whence q = √ (F * r ^ 2 / k).

Calculation: q = √ (5.8 * 10 ^ -5 * 12 / (9 * 10 ^ 9)) = 8 * 10 ^ -8 C = 80 nC.

Answer: Each of the bodies carries a charge of 80 nC.