Which of the following is the correct vector form of the Coulomb force exerted on q2 by q1?

Which of the following is the correct vector form of the Coulomb force exerted on q2 by q1?

• A. F21 = k q1 q2 (r2 − r1) / |r2 − r1|^3
• B. F21 = k q1 q2 (r1 − r2) / |r2 − r1|^3
• C. F21 = k q1 q2 (r2 − r1) / |r1 − r2|^3
• D. F21 = k q1 q2 (r1 − r2) / |r1 − r2|^3

Answer: (A)

Coulomb’s law in vector form says the force on charge q2 due to q1 points along the line from q1 to q2 and has magnitude k|q1 q2|/r^2, where r is the distance between them. Writing this as a vector gives F21 = k q1 q2 (r2 − r1) / |r2 − r1|^3. Here, the displacement r2 − r1 points from q1 to q2, so the force on q2 sits along that direction, with the sign set by the product q1 q2: same-sign charges push q2 away from q1, opposite-sign charges pull it toward q1. If you try the form with r1 − r2 in the numerator, you’d flip the direction, which doesn’t match the force on q2 due to q1. The distance in the denominator is the same either way because |r1 − r2| = |r2 − r1|, so the only difference between those variants is the direction encoded by the vector part.

Coulomb’s law in vector form says the force on charge q2 due to q1 points along the line from q1 to q2 and has magnitude k|q1 q2|/r^2, where r is the distance between them. Writing this as a vector gives F21 = k q1 q2 (r2 − r1) / |r2 − r1|^3. Here, the displacement r2 − r1 points from q1 to q2, so the force on q2 sits along that direction, with the sign set by the product q1 q2: same-sign charges push q2 away from q1, opposite-sign charges pull it toward q1. If you try the form with r1 − r2 in the numerator, you’d flip the direction, which doesn’t match the force on q2 due to q1. The distance in the denominator is the same either way because |r1 − r2| = |r2 − r1|, so the only difference between those variants is the direction encoded by the vector part.