# Force that surrounds two like charges and two opposite charges

If |-q||-q| = |q||-q|, is the force that surrounds a) two like charges -q and -q (which are 100 centimeters apart) less than the force that surrounds b) two opposite charges q and -q (which are also 100 cm apart)? Using the formula of force due to a point charge, $$F = \frac{k q_1 q_2}{r^2}$$ we could find a and b have the same force that surrounds them but in simulation, the equipotentials of two like charges in a single configuration are farther than the equipotentials of two opposite charges in other configurations. Does this imply that the electric force that surrounds the two opposite charges is greater? What could explain the difference in spacing of equipotentials in these two configurations?

two positive charges

two opposite charges

1. "the force that surrounds" - Force doesn't surround anything. Force acts on things. With two point-like charges (call them A and B), charge B has a force acting on it due the its interaction with the electric field due to A at B's location. Likewise for A interacting with the field of B.

2. The magnitude of the force of $$q$$ on $$-q$$ is the same as the magnitude for $$q$$ on $$q$$. The negative sign difference of the forces denotes a direction for the force. Because we don't know the specific locations in space of your charges (are the two arrangements co-linear?) we can't say anything about directional comparisons.

3. Equipotentials are not forces. The patterns of the equipotentials for the $$q$$ $$q$$ arrangement will be different from the $$q$$ $$-q$$ configuration. I don't understand what you mean by "farther". The slope across the equipotentials relates to the electric field due to the charges at other locations, but that says nothing about the forces on those 2 charges.

4. You can draw as many equipotentials as you wish. It doesn't matter. Charges don't know anything about equipotentials. Equipotential drawings are for people to help visualize the intensity and direction of electric fields.

• 2. Aren't two point particles automatically co-linear? Commented Mar 22, 2021 at 3:59
• Thank you for the clarification in number 1! By 'farther', I mean that the spacing of equipotential in q q configuration is larger than the spacing in q -q configuration Commented Mar 22, 2021 at 4:42
• @electronpusher Of course. We don't know the comparison of the orientation of the +- pair to the ++ pair. "are the two arrangements co-linear?" Commented Mar 22, 2021 at 12:06

You're looking at a very limited area. Yes, the force in between two unlike charges is much greater, but as you move further away from the charges, the E field falls off like $$\frac{1}{r^2}$$ for like charges and $$\frac{1}{r^3}$$ for unlike charges since it's electrically neutral.

There will be more overall equipotentials for unlike charges (twice as many), but the energy stored in the fields is the same.