Thermodynamics, Electricity, and Magnetism/Electric Charge

Electric charge occurs in two forms: positive and negative. The general rule of charges is "opposites attract, likes repel" - in other words, charges of the same sign repel each other, while charges of unlike or opposite signs attract each other. The SI unit for charge is the coulomb (C); 1 coulomb is the amount of electric charge transported by a steady current of one ampere (A) in one second (s).

How various materials act under the influence of electric forces is often linked to how easily electrons are dislodged from their constituent atoms/molecules and move through the material. Materials which conduct electric charge well are called "conductors". while those which are not are called "insulators". Metals are typically good conductors, while many non-metals are insulators.

An electron has an electric charge of -e, while a proton has an electric charge of +e, with $e=1.602*10^{-19}C$ .

Electric charge in matter is generally quantized in multiples of e. The net charge before a given interaction is the same as the net charge after that interaction, so charge is conserved.

Coulomb's Law explains that the electric, or Coulomb, force exerted by a point charge q₂ on another point charge q₁, separated from q₂ by a distance of r_{1 2}, is given by ${F}_{12}={1 \over 4\pi \varepsilon _{0}}{q_{1}q_{2} \over r_{12}^{2}}{\hat {r}}_{12}\$ , in which $1 \over 4\pi \varepsilon _{0}$ sets the unit of charge.

The superposition principle - which states that for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually - applies when multiple charges are present. The electric forces on a particular point charge q due to all other charges add together vectorially. For continuous charge distributions, this addition is done by integration; the force of such a distribution on the point charge q depends on the particular charge distribution.

For charges distributed on a line, the force on the point charge q due to the distribution is ${F}={q \over 4\pi \varepsilon _{0}}\int {{\hat {r}}'}{{\lambda (x)dx} \over {r'}^{2}}\$ , where $\lambda$ is the one-dimensional charge density.

For charges distributed over a surface, the force on the point charge q due to the distribution is ${F}={q \over 4\pi \varepsilon _{0}}\int _{surface}{{\hat {r}}'}{{\sigma (x)dx} \over {r'}^{2}}\$ , where $\sigma$ is the two-dimensional charge density.

For charges distributed through a volume, the force on the point charge q due to the distribution is ${F}={q \over 4\pi \varepsilon _{0}}\int _{volume}{{\hat {r}}'}{{\rho (x)dx} \over {r'}^{2}}\$ , where $\rho$ is the three-dimensional charge density.

Electric forces are generally much stronger than gravitational forces, except on the astronomical scale. These forces are responsible for the stability of atoms, molecules, solids, and liquids. Electrical interactions are also the cause of all chemical reactions and biological processes.

External Links

• Reference Tools & Resources for Chapter 21 of Physics for Scientists and Engineers with Modern Physics, 3rd ed. by Fishbane, Gasiorowicz, and Thornton.