Electric charge is fundamental property of subatomic particles and explains the interaction of charged particles with each other as well as with electric and magnetic fields.

Charge is expressed in Coulomb $\left(C\right)$, is usually denoted by the letter $q$, and has the following properties.

Charge is a number:

It can be positive, negative, or equal to zero. A particle (neutron) or an object with zero net charge is said to be neutral. It then either has no charge whatsoever or carries the same number of protons and electrons which causes the net charge to be zero.

Charge is quantized:

It can only exist in amounts equal to an integer multiple of the elementary charge $e$ where

\boxed{e=1.6\times {10}^{-19}\ \ \ C}

All protons contain the smallest amount of positive charge that can be found in nature which is equal to

\boxed{q_p=+e}

All electrons contain the smallest amount of negative charge that can be found in nature which is equal to

\boxed{q_e=-e}

In practice, the elementary charge $e$ is a useful quantity especially when dealing with protons and electrons. The proper SI unit for charge is the coulomb however and one coulomb of charge is equal to

1\ C=6.2\times {10}^{18}e

Charge is additive:

The net charge on an object is equal to the sum of the individual charges it contains.

A net charge arises when an object has an excess of protons (net positive charge) or electrons (net negative charge). Since charge can only exist in integer amounts of $\pm e$, the net charge on an object must be either an integer multiple of $e$ or zero.

For example, an object with $10$ protons and $8$ electrons would have a net charge equal to

q_{net}=10e+8\cdot \left(-e\right)=10e-8e=2e

Note: because the fundamental charge $e$ is such a small value, an object can, in practice, have almost any value of charge within a precision of $1.6\times {10}^{-19}\ C$.

Charge is conserved:

It cannot be created or destroyed but simply moved around or separated from one object to another. As such, the net charge of an object is conserved if the object does not undergo any interaction with another object.

In the previous experiment, the total charge carried by the glass rod and the silk cloth remained constant while the cloth was removing electrons from the glass rod: any electron lost by the glass rod was transferred to the cloth.

Charge within materials and classic charge distributions:

Different types of materials have different properties when it comes to the charge that they carry.

Perfect Insulator: the charges contained in a perfect insulator a fixed in place and cannot move (much like candied fruit in cake). Styrofoam, plastic, rubber, dry air etc. are all examples of insulators.

Dielectric: the charges, or combination of charges, are fixed in place but free to rotate when placed in an electric field (with which they align). Glass, plastic, mica, ceramic, etc. are all examples of dielectrics.

Conductor: the charges contained in a perfect conductor are free to move through the conducting material and any net charge on a conductor lives on its outer surface (to minimize repulsion). In general, any metal is a conductor.

In addition, placing another source of charge near a conductor will induce charge separation in the conductor as shown in the experiment below. A neutral piece of copper is suspended from a thread and a positively charged glass rod is brought near the copper rod without being allowed to touch it.

Observation: despite the copper rod being neutral, it is slightly attracted to the positive glass rod.

Explanation: the neutral copper rod carries the same amount of positive charge as negative charge and is therefore neutral. When the positively charged glass rod is brought closer, it repels the positive charges in the copper rod and they flow freely to the opposite end of the copper rod. Simultaneously, the negative charges in the copper rod are attracted to the glass rod and accumulate on the opposite end. The positive charges in the glass rod then attract the negative charges in the copper rod slightly more than they repel the positive charges (which are further away): the net effect is a weak attraction of the copper rod, even though it is neutral! This phenomenon is common to all conductors and is called induced charge separation.

Classic distributions of charge

Point charge: a point charge is a mathematical point carrying a charge $q$. A point charge — sometimes called a monopole — has not top, bottom, front, or back and is an idealization often used to describe fundamental particles likes protons or electrons.

Electric dipole: two point charges with opposite charge $+q$ and $-q$ separated by a fixed distance $d$ is called an electric dipole.

Linear charge density $\lambda $: a charge $Q$ distributed over a length $L$ is best described by a linear charge density $\lambda $ defined by

\boxed{\lambda =\frac{Q}{L}\ \ \ \ \left(C/m\right)}

This quantity represents the amount of charge per unit length and is useful when charge is distributed on an infinite wire or similar one-dimensional object.

Surface charge density $\sigma $: a charge $Q$ distributed over an area $A$ is best described by a surface charge density $\sigma $ defined by

\boxed{\sigma =\frac{Q}{A}\ \ \ \ \left(C/m^2\right)}

This quantity represents the amount of charge per unit area and is useful when charge is distributed over an infinite sheet or similar two-dimensional object.

Volume charge density $\rho $: a charge $Q$ distributed over a volume $V$ is best described by a volume charge density $\rho $ defined by

\boxed{\rho =\frac{Q}{V}\ \ \ \ \left(C/m^3\right)}

This quantity represents the amount of charge per unit volume.

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