电荷之间的静电力：库仑定律

Objects with electric charge exert a force on each other due to their electric charge. This force is called the electrostatic force. Coulomb's Law provides a very accurate way of finding both the direction and magnitude of this force; every scientific experiment has upheld Coulomb's Law.

Suppose that we have $2$ charges, $q_1$ and $q_2$, which are separated by a distance $d$. Let the unit vector pointing from $q_1$ to $q_2$ be $\vec{r}$. Then Coulomb's Law states that the electrostatic force $\vec{F}$ that $q_1$ exerts on $q_2$ may be expressed as follows: $$\vec{F}=\frac{kq_1q_2}{d^2}\vec{r}$$ where $k$ is a constant called Coulomb's constant.

Note that $q_2$ also exerts a force on $q_1$, with exactly the same magnitude but opposite direction. If you forget this, just use Newton's Third Law!

Do you see the similarity to gravity? Recall that gravity is also an inverse-square force. Moreover, the electrostatic force is proportional to the charges, in much the same way that the gravitational force is proportional to the masses.

This also means that electrostatic forces are conservative; this is a very big deal!

The value of Coulomb's constant is: $$k\approx 8.987\times 10^9 \frac{N\cdot m^2}{C^2}$$ The units are required to make the equation dimensionally correct, but don't worry about them too much.

Note the power of $10$ in the value of $k$, and compare this to that of $G$, the gravitational constant. Why is $k$ so huge, while $G$ is so tiny?

It turns out that this is because the electrostatic force is much, much stronger than the gravitational force. Later on, you may learn about the four fundamental forces, and how gravity is the weakest one.

The reason that we generally do not have to worry about this either is that, unlike masses, charges can be both positive and negative. This means that on any decently large scale, the positive and negative forces tend to cancel out, resulting in a lack of electrostatic force. On the other hand, mass is always positive, meaning that it can make a huge difference on a large scale.

Thus, the electrostatic force is mostly small-scale, but on the atomic scale, it definitely overwhelms gravity.