F_e = (1 / (4 p e₀))(q₁ q₂ / R²)

q₁, q₂ electric charges
e₀ = 8.854 × 10^-12 Coul/(N m)

Thus just as gravity creates a gravitational field, electricity creates an electric field. This similarity is probably related to a universal Law relating such attractive and repelling forces, which may not be presently understood. I can continue such discussion, which I don't presently believe is very relevant here. I state it that way because perhaps the universal Law I mention (if such exists) would be very relevant regarding basic causes of weather. Presently, the greatest relevance of atmospheric electricity is lightning, which I believe is the #1 killer from thunderstorms. Many other electronics-related topics can be mentioned - voltage, resistance, capacitance, direct and alternating current, etc., which are very important if you want to build a weather station...but if not, let's blissfully ignore them & proceed

Magnetism You are probably familiar with attractive & repelling forces of magnets. Similarly with electric charges, magnetic forces are defined; one side of a magnet arbitrarily called north (N), the other south (S). Magnetic field strength can be measured using electric charge, suggesting a relation among them. If a fundamental charge q₀ moves thru a magnetic field with strength B with velocity V, a force (F_B) acts on the charge :

F_B = q₀ V × B

Unlike electric charges though, isolated magnetic poles evidently do not exist. If a magnetic N pole exists, an associated S pole does also, which together are called a dipole. Lines of force connect the dipole, arbitrarily from S to N, similarly as electric current flowing from - to + charges. If such a dipole (e.g., a compass needle) is placed in an external magnetic field (e.g., Earth's), a torque (T) acts on the dipole so that its N pole faces the external S pole (opposites attract, likes repel), and vice-versa :

T = µ × B

µ : magnetic dipole moment

Magnetic dipole moment is a vector a similar way electric current is. A group of electrons can combine to make a total charge many, many times the fundamental charge, and flow as a current, direction of flow defining direction of the electric field vector. Similarly, a magnetic vector is defined, strength of the dipole (moment) similar with charge strength. Earth's magnetic field is relatively weak at any location, but strong considering how far we are from the poles (which I think originate from rotation of molten metals of Earth's interior - geology is not my specialty). It is µ_Earth = 8.0 × 10^-22 J/T. T (Tesla) is a symbol for units of magnetic flux density, equivalent MKS base units being kg/(Coul sec). Presently, Earth's magnetic N pole is located in Greenland and the S pole in Antarctica. I.e., these do not correspond exactly with North and South poles as Earth's rotation axis define, such that an adjustment should be made when using a compass, depending with your location.

The Maxwell Equations James Clerk Maxwell is attributed with unification of electric and magnetic theories and observations as a set of equations known as the Maxwell Equations. They are :

Gauss' Law for Electricity

§ E · dl = - dF_B/dt

l : current loop vector
F_B : magnetic field strength
t : time

This describes the electrical effect of changing a magnetic field. The critical experiment supporting this is the observation that a bar magnet thrust thru a conducting wire loop produces an electric current in the loop.

Ampere's Law (Maxwell's extension)

§ B · dl = µ₀ e₀ dF_E/dt + µ₀ i

F_E : electric field strength
µ₀ : permeability constant = 4 PI × 10^-7 T m/A
i : conduction current

This describes the magnetic effect of changing an electric field or current. The critical experiments supporting this are 1) a current flowing in a wire loop creates a magnetic field 2) The speed of light can be measured from purely electromagnetic measurements.

Among the most relevant consequences of this is that Earth's magnetic field protects us from harmful charged particles flowing from our sun, diverting them around Earth. These set of equations describe electromagnetic theory. Energy is often transported as alternating electric and magnetic waves - electromagnetic radiation. All bodies radiate according to their temperature and emissivity (which I hope to discuss later). Maxwell showed that speed of such waves is determined as :

c = 1 / (µ₀ e₀)^½

c : light speed = 3.00 × 10⁸ m/sec

Energy of such waves is determined as:

S = (1 / µ₀) E × B

S : Poynting vector (different than S above)

The Poynting vector specifies magnitude (energy flux, e.g., W/m²) and direction of electromagnetic wave propagation.

Equation for Relative Speed If object A moves 30 m/sec to one direction (relative with an observer) and object B moves 10 m/sec to the opposite direction, what is their speed relative with each other? You may say 40 m/sec, stating that 10 m/sec + 30 m/sec = 40 m/sec. What if object A's speed is 2.7 × 10⁸ m/sec & object B's 1.8 × 10⁸ m/sec ? Is relative speed 4.5× 10⁸ m/sec ? Can relative speed be greater than light speed? Experience indicates that velocities are additive, but relativity theory states that such indication is deceiving, a consequence of nearly all human experience occurring with speeds much less than light speed. The equation for relative 'linear' speed (SP) of objects A & B is :

SP = (SP_A - SP_B) / (1 - (SP_A SP_B) / c²)

Now what is the answer to the questions above? For the first situation (MKS units used) :

SP_A = 30 (arbitrarily positive direction)
SP_B = -10

SP = (30 - (-10)) / (1 - (30)(-10) / (3.00 × 10⁸)²) = 39.999999999999867 m/sec

For the second situation:

SP_A = 2.7 × 10⁸
SP_B = -1.8 × 10⁸

SP = (2.7 × 10⁸ - (-1.8 × 10⁸)) / (1 - (2.7 × 10⁸)(-1.8 × 10⁸) / (3.00 × 10⁸)²) = 2.922 × 10⁸ m/sec

I.e., for small speeds such that we are accustomed to, the experience of additive speeds very nearly agrees with relativity theory, but approaching light speeds, such is evidently quite incorrect. For comparison, a polar orbiting Earth satellite typically travels about 7000 m/sec, .000023 × light speed! I mention this not because it corrupts wind speed etc. calculations so much as so you are aware (if you weren't) of the presumed character of speed.

Text is copyright of Joseph Bartlo, though may be used with proper crediting.