# Coulomb's law: Is $F_1$ equal to $F_2$ even if $q_1$ is not equal to $q_2$?

I am learning the Coulomb's law. So I have question, If $$q_2$$ be 4 times more than $$q_1$$, would the force from $$q_1$$ to $$q_2$$, still be equal to the force that pushes from $$q_2$$ to $$q_1$$?

As an aside: The force F on an electric charge $$q$$ in an electric field E is F = $$q$$ E.

For two charges $$q_1, q_2$$ separated by a distance $$r$$ you can think of it in two ways:

(1) The first charge creates an electric field E$$_1$$ = $$q_1 /4 \pi \epsilon_0 r^2$$ at the second charge and the force experienced by this charge is $$q_2 E_1$$.

(2) The second charge creates an electric field E$$_2$$ = $$q_2 / 4 \pi \epsilon_0 r^2$$ at the first charge and the force experienced by this charge is $$q_1 E_2$$.

(forgetting about vectors for the moment)

In both cases the result is $$q_1 q_2 / 4 \pi \epsilon_0 r^2$$

When you take into account the direction of the electric fields you see that the forces are equal in magnitude but in opposite directions.

Yes. That is from Newton's third law, which is experimentally derived. Equal in magnitude, opposite in direction.

• I think you mean third law.
– J.G.
Sep 25, 2022 at 9:22