Section 21.10 Coulomb’s Law
Subsubsection Key Ideas
Definition 21.10.2. Coulomb’s Law.
Coulomb’s law describes the electric force between two stationary point charges interacting through the electric field. The force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between the two charges
\begin{equation*}
\vec{F}_E(r) = q\vec{E}= k \frac{qQ}{r^2} \hat{r}
\end{equation*}
where \(\hat{r}\) is a unit vector that points from point charge to the other, \(r\) is the separation distance between the two charges, and \(k \) is the electrostatic constant. \(Q\) and \(q\) denote that the two charges can have different amounts of charge.
Historical Note 21.10.3.
The force between two point charges was experimentally observed and measured in 1785 by the French scientist Charles Augustin Coulomb. This force is referred to as Coulomb’s Law.
Analogy with Gravity.
Compare the Universal Law of Gravity to Coulomb’s Law:
\begin{equation*}
\vec{F}_G(r) = m\vec{g} = -G \frac{mM}{r^2} \hat{r}
\end{equation*}
\begin{equation*}
\vec{F}_E(r) = q\vec{E}= k \frac{qQ}{r^2} \hat{r}
\end{equation*}
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Both laws define force: one between point masses, the other between point charges.
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Both are inverse square laws. The forces are proportional to the inverse square of the distance between the objects.
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The forces defined by both laws are central forces meaning that the forces act along a line joining the center of the two objects.
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Both force laws are conservative forces meaning the work done by these forces is independent of the path followed by the object. The work only depends on the initial and final position of the object while under the influence of the force.
A consequence of these similarities is that many physical and mathematical tools apply to both. If you have many charges then the principle of superposition determines the net effect of many charges or masses interacting, as you will see in the next chapter.
Subsubsection Activities
Activity 21.10.1. Equal and Opposite.
Explain how Coulomb’s Law is consistent with Newton’s third law, which states that the forces on the two charges should be equal in magnitude and opposite in direction. Check both the case that the charges have the same sign and the case that the charges have unlike sign.
Explanation 21.10.2. Three Charges.
Shown below are three point charges (A, B, and C). Is the magnitude of the net electric force on charge A greater than, less than, or equal to the magnitude of the net electric force on charge C? Explain your reasoning.
