Charges

The SI units for charge Q is the Coulomb. Charge is quantised, meaning the charge of anything is an integer multiple of $e/3$; this is an experimental fact, and there is no well-understood reason for why yet. The charges of the proton and electron are exactly opposite: $\pm 1.602\ast 10^{19}C$ Charge is conserved, meaning that new charge can’t be created. Like charges repel, while opposite charges attract. The way we ‘create’ or ‘remove’ charges is by moving them, or separating already-existing positive and negative charges.

Coulomb’s Law

The Coulomb force of one object on another is defined by the following: ${\vec{F}}_{1,2}=k\frac{q_1{q}_2}{r^2}{\hat{r}}_{1,2}$ Where $q$ is the charge of each object, $\hat{r}$ is the unit vector pointing in the direction of object 1 to object 2 , and $r$ being the distance between. Thus, the force by one charge on the other is always along a line that’d connect the two, and whether the force vector on one charge points towards or away from the other depends on whether they’re different polarities or not.

(This is similar to the gravitational force between two objects, but gravitation can only be attractive.)

$k$ is a fundamental constant of nature known as Coulomb’s constant: $k\approx 9\times 10^9\frac{N\cdot m^2}{C^2}$ This is altogether is called Coulomb’s Law.

In terms of the speed of light, $k=c^2\times 10^{-7}\frac{N\cdot s^2}{C^2}$

Reiterating in detail, the general form of Coulomb’s Law in terms of vacuum permittivity: $\overrightarrow{F_e}=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}\hat{r}$ Where:

• $\overrightarrow{F_e}$ is the vector representing the Coulomb force.
• ${ϵ}_0$ is the vacuum permittivity with a value of $8.854\times 10^{-12},\text{F}\cdot {\text{m}}^{-1}$.
• $q_1$ and $q_2$ are the signed magnitudes of the charges.
• $\hat{r}$ is the unit vector pointing from $q_1$ to $q_2$.
• $r$ is the distance between the charges.

physics electricity