Which expression gives the magnitude of the electrostatic force between two point charges according to Coulomb's law?

Which expression gives the magnitude of the electrostatic force between two point charges according to Coulomb's law?

• A. F = k q1 q2 / r^2
• B. F = k q1 q2 / r
• C. F = k q1 q2 (r2 − r1) / |r2 − r1|^3
• D. F = k q1 q2 / |r2 − r1|

Answer: (A)

Coulomb’s law tells us that the force between two point charges depends on how big the charges are and how far apart they are, falling off with the square of the separation and pointing along the line between the charges. For the magnitude, you use the product of the charges and divide by the square of the distance, with the constant k setting the units: F = k |q1 q2| / r^2. If you treat q1 and q2 as magnitudes, that becomes F = k q1 q2 / r^2. The direction isn’t part of the magnitude, but the force acts along the line connecting the charges, repulsive for like charges and attractive for opposite charges. The other forms miss the essential 1/r^2 dependence for the magnitude, or they describe the vector form (which includes direction) rather than the scalar magnitude. The expression with only 1/r, or with no square in the denominator, does not match Coulomb’s law.

Coulomb’s law tells us that the force between two point charges depends on how big the charges are and how far apart they are, falling off with the square of the separation and pointing along the line between the charges. For the magnitude, you use the product of the charges and divide by the square of the distance, with the constant k setting the units: F = k |q1 q2| / r^2. If you treat q1 and q2 as magnitudes, that becomes F = k q1 q2 / r^2. The direction isn’t part of the magnitude, but the force acts along the line connecting the charges, repulsive for like charges and attractive for opposite charges.

The other forms miss the essential 1/r^2 dependence for the magnitude, or they describe the vector form (which includes direction) rather than the scalar magnitude. The expression with only 1/r, or with no square in the denominator, does not match Coulomb’s law.