Electromagnetic force

From (The Plasma Universe Wikipedia-like Encyclopedia)

The Sun's immense gravity is unable to hang onto the "solar wind" which streams away at about 400km per second

The Electromagnetic force is that which occurs when an electromagnetic field interacts with electrically charged particles, such as those that make up a plasma (ie. electrons, protons and other ions).

Plasmas interact strongly with electromagnetic forces, resulting in complexity in structure and motion that far exceeds that found in gases, liquids, and solids.

The formula that describe the behavior of electric and magnetic fields, and their interactions with matter, were derived by Oliver Heaviside (1831-1925), but are now called Maxwell's equations after James Clerk Maxwell (1831–1879).

Comparison with the gravitational force

Between charged particles

Between two charged particles, the electromagnetic force is 36 - 39 orders of magnitude greater than the gravitatiοnal force:

"The basic force law is

where G is the gravitational constant. The force between two objects separated a distance r is

where m₁ and m₂ are the respective masses of the objects. As G is assumed constant, all interpretations of observed astrophysical forces F are then determined by m. [..] For plasma [..] the force laws are given by:

where E, B, and v are the electric and magnetic field strengths, and the plasma velocity across field lines, respectively. The force between charges q is

where ε₀ is the permittivity of free space. When the charges q are in motion with velocity ν, the forces between the resulting currents I = qν are

It is noteworthy that Equations (4) and (5) are inherently 10³⁶ - 10³⁹ orders of magnitude stronger than are Equations (1) and (2). It is especially noteworthy that Equation (5) follows an r^-1 dependency instead of the r^-2 dependencies of the gravitational and electrostatic force laws Equations (2) and (4), making it the longest range force law in the universe. In addition, Equation (5) can be positive in sign, i.e., repulsive, when the interacting currents flow in the opposite sense.^[1]

In a partially ionized plasma

Even in a partially ionized plasma, the force on a charged particle by a magnetic field is significant:

"The basic reason why electromagnetic phenomena are so important in cosmical physics is that there exist celestial magnetic fields which affect the motion of charged particles in space. Under certain conditions electromagnetic forces are much stronger than gravitation. In order to illustrate this, let us suppose that a particle moves at the earth's solar distance R_E ((the position vector being R_E) with the earth's orbital velocity v. If the particle is a neutral hydrogen atom, it is acted upon only by the solar gravitation (the effect of a magnetic field upon a possible atomic magnetic moment being negligible). If M is the solar and m, the atomic mass, and γ is the constant of gravitation, this force is f = -γMm R_E/R_E³. If the atom becomes singly ionized, the ion as well as the electron (charge e = ± 4.8 x 10^-10 e.s.u.) is subject to the force f_m = e(v/c) x B from an interplanetary magnetic field which near the earth's orbit is B. The strength of the interplanetary magnetic field is of the order of 10^-4 gauss, which gives f_m/f ≈ 10⁷. This illustrates the enormous importance of interplanetary and interstellar magnetic fields, compared to gravitation, as long as the matter is ionized.^[2]

Even weakly ionized plasma reacts strongly to electromagnefic fields.

Which force dominates?

A. Ferrari notes:

"Stars are dominated by gravitation, but their surface activity is due to electromagnetic forces. Similarly, the interstellar and intergalactic matter are shaped by plasma forces; and galaxies also show plasma collective behavior where long-range forces are gravitational forces acting on a gas of stars. Active stars (pulsars, X-ray binaries, transient sources, etc) and active galactic nuclei appear to be dominated by plasma effects".^[3]

Electromagnetic field

The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction, one of the four fundamental forces of nature (including gravitation, the weak interaction, and the strong interaction). The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz Force Law.

The behavior of the electromagnetic field can be resolved into four different parts of a loop: (1) the electric and magnetic fields are generated by electric charges, (2) the electric and magnetic fields interact only with each other, (3) the electric and magnetic fields produce forces on electric charges, (4) the electric charges move in space.

A particle at rest feels only the force due to the electric field.

Acceleration

"Only electric fields can accelerate charged particles. Gravity is too weak by several orders of magnitude, and collisions are much to rare"^[4]

A magnetic field produces a force that is always perpendicular to path that a charge follows. Since the magnetic force always acts at right angles to the motion of a charge, it can only turn the charge, it cannot do work on the charge.

A changing magnetic field also produces an electric field (Faraday's Law).

Footnotes