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The simplest case of a magnetic field from an electrical current is a straight wire:

B  is the magnetic field strength, direction according to the Right-Hand-Rule¹
I  is the current
d  is some distance from the wire
u₀  is the permeability of free space (a physical constant)

The above equation shows that the magnetic field strength B becomes less the farther the distance d from the wire (as you would normally think).

the magnetic field strength (also derived from the Biot-Savart law ²) is expressed as:

The above gives the magnetic field strength at the center of the loop where it is found to be the greatest. This has been verified by experiment and is because the concentric field lines become concentrated at the center.

These two equations, for a straight line current and a loop current, provide important information in the interest of designing artificial magnetic fields on a Moon Base, and in fact, appear to show in favor of accomplishing this. This is normally reasoned because a loop current is strongest at the center and a straight-wire current is strongest nearest the wire. This allows design optimizations using large and small circular-conduits and recalling that for a large circle, a section of arc is nearly a straight line.

To complete our discussion of practical formulas, when using multiple loops of wire the equation becomes:

Also, magnetic fields can combine and add together if the current directions are the same for each magnetic field. Likewise, magnetic fields cancel each other if the currents are in opposite directions.

Due to realistic design practices, .. designing magnetic fields will most likely be decided by measuring the magnetic field strengths.

Due to realistic design practices, and the mystery of magnetism, the results of designing magnetic fields will most likely be decided by measuring the magnetic field strengths. However, field strength can easily be measured with a magnetometer or Gaussmeter.3 Earth’s magnetic field varies from 0.25 to 0.65 Gauss, which can be used as a general criteria for designing artificial magnetic fields on the Moon or on a lunar space station.

Magnetic fields will be used to deflect incoming galactic cosmic radiation, which is also a measurable entity. A well known instrument that can be used for measuring cosmic radiation is the geiger counter, but also scintillion counters, semiconductor detectors, or specialized dosimeters. The amount of cosmic rays reaching Earth exposes a human to about 0.33 millisieverts (mSv) per year, which can be referred to for designing magnetic fields.

On Earth, magnetic fields are mostly associated with electric motors, industrial magnets, or for medical specialties such as MRI (Magnetic Resonance Imaging). Otherwise, there is no motive to develop magnetic fields on Earth since it would only have a negative impact on our health. In fact, our main concern on Earth is to reduce EMFs (electromagnetic fields) and there are countless warnings to safeguard ourselves from the EMFs related to electrical equipment or high current sources. One of these are the overhead power lines which are raised high above the ground and designed with cancellation techniques to reduce the EMFs. On Earth, EMF carries a “negative tag” since any additional fields added to our Earth’s magnetic field is considered unhealthy.

But for the endeavor of occupying the Moon or traveling further into Space, we are faced with creating EMFs for protection against cosmic rays. Our situation on Earth is not the same as in Space, which explains why designing magnetic fields has been an underdeveloped technology.

These two equations, .. provide important information in the interest of designing artificial magnetic fields on a Moon Base, and in fact, appear to show in favor of accomplishing this.

1. The Right-Hand-Rule in Magnetic Fields (a natural physical phenomenon) has prompted humorous remarks that the Creator was right-handed.

2. The Biot-Savart law describes a magnetic field generated by a constant electric current and is named after Jean-Baptiste Biot and Felix Savart in 1820.

3. The simplest magnetometer can be found on a smartphone App. Smartphones use the Hall effect, which are built into most mobile devices. To measure the Earth’s magnetic field, make sure the App yields raw data but can also cancel the effects of the phone itself. For example, the magnetic field strength for Los Angeles is typically measured as 0.48 Gauss (or 4.8 x 10^-5 Tesla) and the magnetic field strength for New York City is 0.51 Gauss. Earth’s magnetic field is strongest at the Poles (0.6 Gauss) and weakest at the Equator (0.35 Gauss).