What's the Direction of Force Between Like and Unlike Electric Charges?

Like electric charges repel, while unlike electric charges attract. The electric force on each charge acts along the straight line joining the two charges.

The Reasoning

This is part of D.2 Electric and magnetic fields and applies to both SL and HL. There are two types of electric charge: positive and negative.

The magnitude of the force between two point charges is given by Coulomb's law:

$$F = k\frac{|q_1q_2|}{r^2}$$

Here, $q_1$ and $q_2$ are the charges, $r$ is their separation, and $k$ is the Coulomb constant. The absolute value gives the positive magnitude of the force; the charge signs are then used to determine whether the force is attractive or repulsive.

For example, suppose $q_1=+2.0\,\mu\text{C}$ is to the left of $q_2=-3.0\,\mu\text{C}$. Because the charges are unlike, the force on points right, toward , while the force on points left, toward .

Using $r=0.20\,\text{m}$, the shared force magnitude is

$$F=(8.99\times10^9)\frac{(2.0\times10^{-6})(3.0\times10^{-6})}{(0.20)^2}=1.35\,\text{N}.$$

Increasing the separation decreases the force according to the inverse-square relationship; doubling $r$ reduces $F$ to one quarter. This calculation determines magnitude only; the charge signs determine direction.

By Newton's third law, these forces have equal magnitudes but opposite directions. A common misconception is that the larger charge exerts the larger force. This is incorrect: both charges experience forces of the same magnitude, although their accelerations may differ if their masses differ.

Exam Technique

For a State question, write: “Like charges repel; unlike charges attract.” For a direction question, identify the charge signs, draw the line joining them, and place the force arrow on the specified charge. Do not draw both force arrows on one charge.