In the Coulomb force expression F12 = k q1 q2 / r^2 r_hat_12, the unit vector r_hat_12 points from which to which?

In the Coulomb force expression F12 = k q1 q2 / r^2 r_hat_12, the unit vector r_hat_12 points from which to which?

• A. From q2 to q1
• B. From q1 to q2
• C. From the origin to q1
• D. Along the line perpendicular to the separation

Answer: (A)

The force on charge 1 due to charge 2 points along the line joining the two charges, and with the vector defined so that it points from charge 2 toward charge 1. In the expression F12 = k q1 q2 / r^2 times r_hat_12, the unit vector r_hat_12 is the direction from q2 to q1. This setup makes the magnitude k|q1 q2|/r^2 always point along the line between the charges, while the sign of q1 q2 determines whether the force is away from or toward charge 2 (positive product gives a push away from 2; negative product gives a pull toward 2).

The force on charge 1 due to charge 2 points along the line joining the two charges, and with the vector defined so that it points from charge 2 toward charge 1. In the expression F12 = k q1 q2 / r^2 times r_hat_12, the unit vector r_hat_12 is the direction from q2 to q1. This setup makes the magnitude k|q1 q2|/r^2 always point along the line between the charges, while the sign of q1 q2 determines whether the force is away from or toward charge 2 (positive product gives a push away from 2; negative product gives a pull toward 2).