electric_charge

Stan Zurek, Electric charge, Encyclopedia Magnetica, E-Magnetica.pl |

**Electric charge**, typically denoted by ** e** or

Electrostatic field lines around an electric dipole, in which positive and a negative charges attract

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Electric charges have only two types: **positive** or **negative**, with the like polarities repelling each other and the opposite ones attracting.

Every isolated system fulfils the condition of conservation of charge, so that the total sum of positive and negative charges never changes. This is a fundamental law is the basis for all electromagnetic theory.^{2)}

Movement of electric charges constitutes electric current.

Electrical forces in atoms determine the physical and chemical properties of matter.^{3)}

Scientists can describe, but still cannot explain what exactly is electric charge. However, it is sufficient for such a basic property that it exists, it has some physical meaning and is measurable within the given system of units.^{4)}

Opposite charges attract, same charges repel, neutral bodies generate no force (grey) but neutral bodies in the presence of other charges become locally polarised due to electrostatic induction

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For static charges the amount of this force is quantified by Coulomb's law.

The amount of electric charge is quantised and its smallest unit called **elementary charge** has the value of: **e = 1.602 176 634 × 10 ^{−19}** coulomb.

A **proton** has a positive charge of **+e**, and **electron** to the exactly opposite, negative value of **-e** (neutron has zero charge). The matching of the amount of the quantum of positive and negative charges is extremely precise to the highest experimental accuracy that can be attained, at the level of 1 part in 10^{20}. If this was not the case then matter would violently disintegrate.^{7)}^{8)}

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The electric charges in antimatter are reversed, with positron (equivalent of electron) being positive, and antiproton negative. It is possible for positive and negative charges (e.g. electron and positron) to combine and annihilate, converting to other form of energy. It is also possible for two opposing charges to be produced in some sub-atomic interaction. But such interactions always occur in pairs of positive-negative charges, so that the law of charge conservation never violated.^{9)} For example, during radioactive decay it is possible for a positron (e+) to be emitted from a proton (e+), which then becomes a neutron so that the amount of electric charge remains constant.^{10)}

Electrically charged particles also exhibit intrinsic magnetic moment. Electron magnetic moment is especially strong and is responsible for the phenomenon of ferromagnetism.^{11)}

An electric charge generates all of the components of electromagnetic field in the space around itself, depending on the state of motion of the charges:^{12)}^{13)}

- charges which are static in space generate electrostatic field
- charges which move at a constant velocity generate magnetostatic field (due to velocity fields)
- charges which are accelerated generate radiating electromagnetic field (due to acceleration fields)

The presence of a given field can be detect by the amount and direction of mechanical force exerted on another stationary or moving charge (test charge). The total electromagnetic force on an electric charge is called Lorentz force.^{14)}

The name **electrostatic field** is used to denote specifically that some **electric field** does not change with time, because the charges are stationary.^{15)}

An electrostatic field generated by one charge exerts a force on another electric charge, as defined by the Coulomb's law:^{16)}

$$ \vec F = \frac{1}{4 · π · ε_0} · \frac{q_1 · q_2}{r^2} · \vec {\hat r } $$ | (N) |

where: $ε_0$ - permittivity of free space, 8.8541878128 × 10^{-12} (F/m), $q_1$ and $q_2$ - amount of electric charge (C), $r$ - distance between the charges (m), $\vec {\hat r }$ - unit vector in the direction of *r*.

Each electric charge, or a charged object generates an electric field in the space around itself, and this is typically visualised by field lines, which by convention are directed away from a positive charge and towards the negative charge. The charges are the “sources” of these field lines, so that the lines start and end at the charges.

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And in a more general case it is the local electric field *E* which generates the force:^{17)}

$$ \vec F = q · \vec E $$ | (N) |

where: $q$ - charge (C), $\vec E$ - electric field vector (V/m).

A positive electric charge (stationary or moving) is accelerated in the direction of the uniform electric field *E*.

For a negative charge, the directions are reversed.

If the charge is already moving before application of an additional electric field then the acceleration add up vectorially, according to the superposition rule.

An electric charge which moves with a constant velocity (without acceleration) produces a **magnetic field** in the space around itself. For a single moving charge the electric and magnetic field it generates are “attached” to the moving charge (does not radiate away into space), and it is sometimes referred to as velocity field.^{18)}

If the electric charges are static then they do not generate magnetic field, and also the magnetic force does not act on them.

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If there are many moving charges, as for example in a conducting wire, and if the resulting electric current does not change (in space or time) then the produced field is called **magnetostatic field**.^{19)}

Magnetostatic field exerts a force on a moving electric charge, which in the absence of electrostatic field is:^{20)}

$$ \vec F = q · \vec v × \vec B $$ | (N) |

where: $q$ - charge (C), $\vec v$ - moving charge velocity vector (m/s), $\vec B$ - magnetic field vector (T).

The force generated by magnetic field is often called the **magnetic force** and is perpendicular to both the direction of movement of the charged body and the direction of the magnetic field, therefore magnetic field do no work (all work is performed by the electric field).^{21)}

Consequently, if the charge is moving parallel to the magnetic field there is no magnetic force acting on it.

The magnetic force does not accelerate the charge in a linear way, just deflects its path, and can bend it into a circle, with a radius proportional to the velocity of the charge, its mass and intensity of magnetic field.^{22)} If the direction of initial movement is not perpendicular to the magnetic field the the trajectory can be helical.^{23)}

Electric current **I** generates magnetic field strength **H** whose vector is always perpendicular to the direction of I, according to the right-hand rule

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Magnetic field around a moving electron (because of the convention the electron moves in the opposite direction to electric current)^{24)}

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**Electromagnetic field** (comprising both components, electric and magnetic) is generated by electric charges whose motion is accelerated in a linear, circular, or any other way (with positive or negative acceleration). Such electromagnetic field radiates into space, away from the accelerated charge.^{25)}

Such electromagnetic field can be also called acceleration field.^{26)}

Electromagnetic field exerts a force on a stationary or moving electric charge, defined by the Lorentz force:^{27)}

$$ \vec F = q · \vec E + q · \vec v × \vec B $$ | (N) |

where: $q$ - charge (C), $\vec E$ - electric field vector (V/m), $\vec v$ - moving charge velocity vector (m/s), $\vec B$ - magnetic field vector (T).

A stationary charge will be moved, because of the electric field, and magnetic field will affect is the path of movement. However, the exact trajectory can be quite complex, depending on the ratio of all the involved quantities, including the direction and velocity of the initial movement.

If the electric field is weak, and the magnetic field strong, the charge can move sideways, along a cycloid curve.^{28)}

Diagram illustrating generation of electromagnetic field by an electric charge: a static charge (grey small circle at the centre) generates electrostatic field (blue area) which statically extends away into space. A sudden acceleration of the charge (dark blue small circle) creates an electromagnetic pulse (red ring) which radiates away into space at the speed of light, and the space far away still contains the electrostatic field from the time when the charge was stationary (as indicated by grey lines). A charge moving at a constant velocity *v* generates electric and magnetic field attached with the charge (green area). The field lines (black lines) show the direction and intensity of electric field.^{29)}

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By convention, direction of electric current is from plus to minus of the voltage source, hence opposite to the movement of electrons

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Electric current is defined as a change of electric charge *Q* in time *t*:

$$ I = \frac{Δ Q}{Δ t} $$ | (A) |

Hence, current is a movement of electric charges, in any unbalanced form: individual charged particles (electrons or ions), unbalanced distribution of charges, virtual or quasi-particles (electron holes), etc.

From a classical physics viewpoint, an electron orbiting an atomic nucleus also constitutes a current, whose value can be calculated knowing dimensions of an atom, speed of orbiting and the value of electric charge of the electron.

The analogy of orbital moment is an electron orbiting the nucleus on a circular orbit (left) and for spin the sphere spins around its own axis (right)

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Therefore, there is a magnetic dipole moment associated with the orbit of an electron: magnetic orbital moment.

A spinning electrically charged body will also generate a magnetic field, and this analogy is used as “illustration” of magnetic spin moment of an electron.

However, this classical analogy fails, because neutrons also have a magnetic spin moment, even though they have no electrical charge.

Only such sub-atomic particles like quarks are thought to have electric electric charge in non-integer quantities e.g. -1/3 *e* or +2/3 *e*, but they only exists in configurations which add up to integer values of charge. For example, proton comprises three quarks (*up, up, down*), which add up to +1 *e*. Therefore, in any macroscopic application the charge is always quantised by the elementary amount of 1 e.^{30)}^{31)}

Existence of quantised **magnetic charges** (magnetic monopoles) was proposed as a theoretical reason for quantisation of electrical charges. However, despite extensive international research no magnetic monopoles were ever found.

Macroscopically observable magnetic properties of materials arise because of the magnetic quantum properties of electrons (spin magnetic moment and orbital magnetic moment), as well as due to the electrostatic interactions between the electron orbitals.^{32)}

electric_charge.txt · Last modified: 2021/04/15 23:42 by stan_zurek

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