Coulomb's Law

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Charge and the electrostatic field

Stepping back a little from the direct solution of Maxwell's Equations, let us try to construct some of the framework underlying them. Most “everyday” electromagnetism relies on the motion of electrons or protons (either singly or as part of atomic nuclei). Electrons carry a charge of $q_e=-1.6\times 10^{-19}$ C while an atomic nucleus would exhibit a charge of $q_N=1.6\times 10^{-19}\cdot N$ C, where $N$ is the atomic number of the element in question. It is interesting to note that charge is one of the universal conserved quantities, like mass and energy. It can be neither created nor destroyed.

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Coulombs law

The simplest system that of two point charges $q 1$ and $q 2$ separated by a distance $r 12$ . Assuming free space (vacuum) surrounding the charges, charge 1 feels a force

$F_1 = -\frac{q_1q_2}{4\pi \epsilon_0 r^2}$

along the line connecting the two charges. Charge 2 experiences the reaction force

$F 2 = - F 1$

along the same connecting line.

Two charges in space that exert forces on each other according to Coulomb's Law.

The negative sign is somewhat arbitrary, in that it depends on the chosen direction of the unit vector that lies along the line that connects the charges.

This central force law is known as Coulomb’s law, in honor of Charles Augustin de Coulomb (1736-1806). Note its similarity to the inverse-square gravitation law of Newton

$F_g = \frac{G m_1m_2}{r^2}$ ,

where $G$ is the universal gravitation constant. Unlike gravity, which is always attractive, the electric force can be attractive (if charges are of opposite sign) or repulsive (if charges are of the same sign).

We can think of a point charge $q 1$ emitting an “electric field”

$\textbf{E} = \frac{q_1}{4\pi \epsilon_0 r^2}\hat{\textbf{r}}$ ,