# How will the force of the Coulomb interaction of two point charges change if the distance

How will the force of the Coulomb interaction of two point charges change if the distance between them decreases by 2 times?

According to Coulomb’s law:
F = k * q1 * q2 / (r ^ 2), where F is the force of the action of the charges on each other, k is the proportionality coefficient, q1, q2 are the magnitudes of the charges, r is the distance between the charges.
Force until distance decreases: F1 = k * q1 * q2 / (r1 ^ 2).
Force after decreasing the distance: F2 = k * q1 * q2 / (r2 ^ 2), where r2 = 0.5 r1; F2 = k * q1 * q2 / ((0.5r2) ^ 2).
Then:
F2 / F21 = (k * q1 * q2 / (0.5r1 ^ 2) / (k * q1 * q2 / (r1 ^ 2)) = (r1 ^ 2) / (0.25r1 ^ 2) = 4.
Answer: The strength of the Coulomb interaction will increase by 4 times.

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