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).
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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