The Significance and Characteristics of the Magnetic Constant in Physics

I. Introduction to Physical Constants

In the realm of physics, a plethora of constants play crucial roles within models designed to elucidate the workings of the universe. These are fixed numerical values incorporated into equations alongside variables. For example, the universal gravitational constant ($G = 6.6743×10^{−11} m^3/kg⋅s^2$) is instrumental in predicting the motion of falling objects.

What is remarkable about these constants is their highly precise yet seemingly arbitrary values. For instance, one may question why the value of the gravitational constant is 6.6743 rather than 6.6744. These constants are not derived from theoretical principles but are determined through measurement. Over time, with the advancement of instrumentation, the precision of these measurements has steadily increased.

II. Electric and Magnetic Constants: Their Significance

Last week, the electric constant, whimsically known as the “permittivity of free space,” was discussed. It is a fundamental parameter that governs, among other things, the interaction between electrons and protons in the formation of molecules, which is of utmost importance for the existence of life, the universe, and all that it encompasses.

Today, the focus is on the magnetic constant, also referred to as the “permeability of free space.” This constant determines the strength of magnetic fields in a vacuum and, by extension, in air. Its significance cannot be overstated. Without magnetic fields, there would be no light in the universe, considering that light is a form of electromagnetic radiation.

Electric and magnetic forces are inherently interconnected. Humans have harnessed this interaction to develop various technologies, such as powering electric motors and generating electricity.

III. A Pragmatical Note on Constant Derivation

It was previously stated that the values of constants are measured rather than derived. However, this is not always entirely accurate. Consider the speed of light ($c$), a fundamental constant. It is related to the electric constant ($\epsilon_0$) and the magnetic constant ($\mu_0$) through an equation. This implies that these three values are not independent; if two are known, the third can be derived.

Physicists define the speed of light as exactly 299,792,458 meters per second. This definition is based on the fact that a meter is defined as the distance light travels in 1/299,792,458 of a second. Subsequently, the magnetic constant ($\mu_0$) is measured, and this value, along with the defined speed of light, is used to calculate the electric constant ($\epsilon_0$). While this may seem like a form of “cheating,” in scientific practice, it is necessary to establish arbitrary units and define certain parameters to commence actual scientific inquiry. In essence, all systems of measurement, like all words, are human - made constructs.

IV. Permeability of Free Space and Magnetic Field Generation

Magnetic fields, denoted by the symbol $B$, can be generated by magnets, as depicted in the accompanying photograph. Due to the interdependence of electric and magnetic phenomena, magnetic fields can also be produced by moving electrical charges (herein referred to as “charges” for simplicity, representing charged particles like electrons). This is described by the Biot - Savart law.

In the equation, the magnetic constant ($\mu_0$) is present, along with the value of the electric charge ($q$) moving at a certain velocity ($v$). The equation indicates that the magnetic field strength increases with the magnitude of the electric charge and decreases with the distance ($r$) from the moving charge. The magnetic constant precisely quantifies this variation.

In practical scenarios, we seldom deal with individual moving electrons. Instead, we frequently encounter streams of moving electrons, which constitute electric current ($I$), a measurable quantity. If the charge on the particles is known in coulombs, the current in amperes is determined by the number of coulombs flowing per second. The equation can be rewritten in terms of current as $B=\frac{\mu_0I}{2\pi r}$.

V. The Ubiquitous Influence of Electric - Magnetic Interaction

The fact that electric current generates a magnetic field finds application in numerous machines. Electromagnets, for example, utilize this principle. In factories and scrapyards, the magnetic force of electromagnets can be switched on and off to manipulate metal objects. Audio speakers also operate on this principle, where an electric signal causes a magnetic driver to vibrate, generating pressure waves in the air to produce sound.

Conversely, magnetic fields influence electric currents, which is the operating principle of motors. In a motor, a current passes through a coil of wire within a magnetic field, typically created by permanent magnets. The force exerted on the coil causes it to rotate, powering various devices such as fan motors, AC compressors, or the main drive of an electric car.

Furthermore, just as a changing electric field generates a magnetic field, a changing magnetic field generates an electric field, which in turn produces an electric current. This is the mechanism behind most power generation. Energy sources like steam, wind, or moving water spin a turbine, which rotates a coil within a magnetic field. The changing magnetic flux induces a voltage in the coil, converting mechanical energy into electrical energy for transmission to homes.

VI. Measuring the Magnetic Constant

One method for measuring the magnetic constant ($\mu_0$) involves the use of a current balance. A simple version consists of two parallel wires carrying electric current ($I$) in opposite directions, suspended by strings to allow for movement.

The current in each wire generates a magnetic field at the location of the other wire, causing the wires to repel each other. As they move apart, the magnetic force decreases, while the horizontal component of the tension in the support string increases due to the change in angle. When these two forces are equal, the wires reach a state of “balance.”

Given the value of the electric current and the distance between the wires ($r$), the magnetic constant ($\mu_0$) can be determined. Subsequently, as previously demonstrated, this value, along with the defined speed of light, can be used to calculate the electric constant ($\epsilon_0$).

According to the International Committee for Weights and Measures, the value of the magnetic constant is $\mu_0 = 1.256637061272×10^{–6} N/A^2$. In conclusion, the magnetic constant is indeed of great importance in the field of physics.