Electromagnetism

Elementary charge

The elementary charge e is the smallest possible unit of charge. It is the charge of a single proton or electron, measured in coulombs. Protons have a charge +e, and electrons have a charge of -e.

e = 1.6\e{-19} \unit{C}

Conversely, the number of electrons in 1 coulomb is 1.6\e{19}.

The charge Q of an object is equal to the difference in the number of protons n to the number of electrons m, times the elementary charge e. This charge must be a multiple of e.

Q = (n - m) \times e

Charges

Charge is always conserved in an isolated system. Electrons move around, but are never created or destroyed.

Same charges repel, and opposite charges attract.

When two objects touch, electrons move between the two until the charges of the objects are equal.

Electrons in an insulator are tightly bound and can’t travel.

Coulomb’s law

The electrostatic force between two charged bodies is proportional to the product of the charges q_1 and q_2, and is inversely proportional to the square of the distance r between the bodies. If the force is positive, the bodies repel each other, and if the force is negative (q_1 and q_2 have opposite signs) they attract.

F = k \frac{q_1 q_2}{r^2}

The constant k is equal to 9\e{9} \unit{Nm}^2 \unit{C}^{-2}.

The electrostatic force is very similar to the gravitational force, but is a lot stronger when the distance is small.