Question

Using Coulomb’s Law, if the distance between two point charges is reduced by a factor of three, by what exact factor does the magnitude of the electrostatic force between them increase?

Accepted Answer

According to Coulomb&#x27;s Law, the electrostatic force between two point charges is inversely proportional to the square of the distance between them, meaning that as distance decreases, force increases according to an inverse-square relationship. This relationship is mathematically expressed as F = k(q1q2)/r², where F is the force, q represents the charges, and r is the distance. If you reduce the distance by a factor of three, the new distance becomes one-third of the original, and since this value must be squared in the denominator, you are dividing the force by (1/3)², which is 1/9. Dividing by a fraction is equivalent to multiplying by its reciprocal, so the force increases by a factor of nine. You can visualize this like the spread of light from a flashlight: if you move twice as close to a wall, the light intensity does not just double, it becomes four times as bright because the light is concentrated into a much smaller area.

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Using Coulomb’s Law, if the distance between two point charges is reduced by a factor of three, by what exact factor does the magnitude of the electrostatic force between them increase?

According to Coulomb's Law, the electrostatic force between two point charges is inversely proportional to the square of the distance between them, meaning that as distance decreases, force increases according to an inverse-square relationship. This relationship is mathematically ex....