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Electric charge

Units of charge

In the SI system, the amount of electric charge Q is measured in coulombs, denoted with the symbol “C”.

However, the base unit of electricity in the SI system is ampere (A), which measures electric current I. The charge Q = 1 C is equal to the amount of charge transferred with the current I = 1 A flowing for the time t = 1 s.

$$Q = I·t $$ (A·s) ≡ (C)

The amount of charge is used for example for quantifying partial discharge phenomena in electrical insulation. Common values of partial discharges are between 1 pC and 10 nC, with values below 10 pC not leading to harmful effects in the the insulating material.

Properties of electric charges

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.. This value is a constant in our universe.

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 1020. If this was not the case then matter would violently disintegrate.

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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. 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.

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

Fields and forces

Electrostatic field

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

An electrostatic field generated by one charge exerts a force on another electric charge, as defined by the Coulomb’s law:

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

(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.

Electrostatic field lines of a positive charge

S. Zurek, E-Magnetica.pl, CC-BY-4.0

Electrostatic field of a negative charge

S. Zurek, E-Magnetica.pl, CC-BY-4.0

Positive charges repel

S. Zurek, E-Magnetica.pl, CC-BY-4.0

Negative charges repel

S. Zurek, E-Magnetica.pl, CC-BY-4.0

e on a positive charge q

Electric field E acting with a force Fon a positive charge q

S. Zurek, E-Magnetica.pl, CC-BY-4.0

And in a more general case it is the local electric field E which generates the force:

$$ \vec F = q · \vec E $$

(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.

Magnetostatic field

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.

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

m on a moving positive charge q

Magnetic field B acting with a force Fon a moving positive charge q

S. Zurek, E-Magnetica.pl, CC-BY-4.0

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.

Magnetostatic field exerts a force on a moving electric charge, which in the absence of electrostatic field is:

$$ \vec F = q · \vec v × \vec B $$

(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).

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. If the direction of initial movement is not perpendicular to the magnetic field the the trajectory can be helical.

I generates H whose vector is always perpendicular to the direction of I, according to the electric_current_generates_magnetic_field_magnetica.jpg

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

S. Zurek, E-Magnetica.pl, CC-BY-4.0

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

S. Zurek, E-Magnetica.pl, CC-BY-4.0

Electromagnetic field

e + Fm on a positive charge q

Electric field E and magnetic field B acting with a force F = F+ Fon a positive charge q

S. Zurek, E-Magnetica.pl, CC-BY-4.0

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.

Such electromagnetic field can be also called acceleration field.

Electromagnetic field exerts a force on a stationary or moving electric charge, defined by the Lorentz force:

$$ \vec F = q · \vec E + q · \vec v × \vec B $$

(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.

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.

S. Zurek, E-Magnetica.pl, CC-BY-4.0

Electric current

Magnetic moments

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)

S. Zurek, E-Magnetica.pl, CC-BY-4.0

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.

Quantisation of electric charges

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.

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.

Magnetism and electromagnetism

Subatomic particle detection

Compact Muon Solenoid () detector at CERN

Many experiments with radioactive matter were conducted by observing the trajectories of particles moving through magnetic and electric field. Devices such as mass spectrometer utilise these effects.

Trajectories of charged particles travelling through magnetic field are bent by the magnetic field due to the Lorentz force: positive particles are deflected one way, negative particles in the opposite way, but the path of photons or uncharged particles is not affected by magnetic field. Additionally, heavy particles are more difficult to deflect, so knowing the velocity and charge it is possible to deduce mass (or charge if the mass is known).

Properties of electrically charged particles are used for detection of sub-atomic particles, in such physical experiments as those carried out in the Large Hadron Collider.

The beams of accelerated particles are made to collide inside a detector, which comprises powerful big superconducting electromagnet (extending over several metres), surrounded by a number of detectors, for sensing various properties of the particles created as an aftermath of the collision. Thousands of single sensors are used around the volume of interest, which allows tracing the trajectories in 3D, and inferring their properties such as momentum, charge, mass, etc.

Schematic overview of ALICE (A Large Ion Collider Experiment)