# magnetic units

If the burden of two systems of measurement for common quantities (English vs. metric) throws your mind into confusion, this is not the place for you! Due to an early lack of standardization in the science of magnetism, we have been plagued with no less than three complete systems of measurement for magnetic quantities.

First, we need to become acquainted with the various quantities associated with magnetism. There ae quite a few more quantities to be dealt with in magnetic systems than for electrical systems. With electricity, the basic quantities are Voltage (E), Current (I), Resistance (R), and Power (P). The first three are related to one another by Ohm’s Law (E=IR ; I=E/R ; R=E/I), while Power is related to voltage, current, and resistance by Joule’s Law (P=IE ; P=I^{2}R ; P=E^{2}/R).

With magnetism, we have the following quantities to deal with:

**Magnetomotive Force** — The quantity of magnetic field force, or “push.” Analogous to electric voltage (electromotive force).

**Field Flux** — The quantity of total field effect, or “substance” of the field. Analogous to electric current.

**Field Intensity** — The amount of field force (mmf) distributed over the length of the electromagnet. Sometimes referred to as *Magnetizing Force*.

**Flux Density** — The amount of magnetic field flux concentrated in a given area.

**Reluctance** — The opposition to magnetic field flux through a given volume of space or material. Analogous to electrical resistance.

**Permeability** — The specific measure of a material’s acceptance of magnetic flux, analogous to the specific resistance of a conductive material (ρ), except inverse (greater permeability means easier passage of magnetic flux, whereas greater specific resistance means more difficult passage of electric current).

Not only do we have more quantities to keep track of with magnetism than with electricity, but we have several different systems of unit measurement for each of these quantities. As with common quantities of length, weight, volume, and temperature, we have both English and metric systems. However, there is actually more than one metric system of units, and multiple metric systems are used in magnetic field measurements! One is called the *cgs*, which stands for **C**entimeter-**G**ram-**S**econd, denoting the root measures upon which the whole system is based. The other was originally known as the *mks* system, which stood for **M**eter-**K**ilogram-**S**econd, which was later revised into another system, called *rmks*, standing for **R**ationalized **M**eter-**K**ilogram-**S**econd. This ended up being adopted as an international standard and renamed *SI* (**S**ysteme **I**nternational).

And yes, the µ symbol is really the same as the metric prefix “micro.” I find this especially confusing, using the exact same alphabetical character to symbolize both a specific quantity and a general metric prefix!

As you might have guessed already, the relationship between field force, field flux, and reluctance is much the same as that between the electrical quantities of electromotive force (E), current (I), and resistance (R). This provides something akin to an Ohm’s Law for magnetic circuits:

And, given that permeability is inversely analogous to specific resistance, the equation for finding the reluctance of a magnetic material is very similar to that for finding the resistance of a conductor:

In either case, a longer piece of material provides a greater opposition, all other factors being equal. Also, a larger cross-sectional area makes for less opposition, all other factors being equal.

The major caveat here is that the reluctance of a material to magnetic flux actually *changes* with the concentration of flux going through it. This makes the “Ohm’s Law” for magnetic circuits nonlinear and far more difficult to work with than the electrical version of Ohm’s Law. It would be analogous to having a resistor that changed resistance as the current through it varied (a circuit composed of *var*istors instead of *res*istors).

**Related**

COMMENTsongsMagnetic Flux is defined also according to a published entropy approach and experimental work as a form of energy or Electromagnetic waves that have magnetic potential, positive or negative [1]. So; the magnetic flux as a flow of energy has to be measured in the same units of energy; i.e. in Joule or as energy flow in Watt. According to a scientific analogy between thermal, electric and magnetic energies and their common effect on an Al‐Fe thermocouple [2]; it was possible to prove that the magnetic potentials could be measured also in Volt as the electric potential or thermal. So, it is possible to recalibrate the already used Gaussmeter to measure the rate of flow of magnetic flux during attraction processes by watt/volt. The reader may follow my proposal for a universal system of units that depends on the analogy between thermal, electric and magnetic energies in a scientific paper and simplify such confusion of units [2]

[1] S. Abdelhady, “A Fundamental Equation of Thermodynamicsthat Embraces Electrical and Magnetic Potentials,”Journal of Electromagnetic Analysis & Applications,Vol. 2, No. 3, 2010, pp. 162-168.

[2] S. Abdelhady, “A Fundamental Equation of Thermodynamics

that Embraces Electrical and Magnetic Potentials,”Journal of Electromagnetic Analysis & Applications,Vol. 2, No. 3, 2010, pp. 162-168.

the definitions of the units of the electric flux or the electric charge and the magnetic flux are misleading. Both should have the same unit of energy per unit area, i.e. Joule/square meter. I hope to read my papers in this corrections:

[1] S. Abdelhady, “An Approach to a Universal System of Units” “J. Electromagnetic Analysis & Applications”, March, 2010, 2: pp.549-556.

[2] S. Abdelhady, “A Fundamental Equation of Thermodynamics that Embraces Electrical and Magnetic Potentials”, “J. Electromagnetic Analysis & Applications”, March, 2010, 2: pp. 162- 166.

[3] S. Abdelhady, “ Comments Concerning Measurements and Equations in Electromagnetism”, “J. Electromagnetic Analysis & Applications”, March, 2010, 2: pp. 677-678.

[4] S. Abdelhady, “An Entropy-Approach to the Duality Property” “J. Electromagnetic Analysis & Applications”, March, 2011, 3: pp.220-227

Regards

Notes on Measurement of Electric Charge and Magnetic Flux

Salama Abdelhady

Department of Mechanical Engineering, CIC, Cairo, Egypt

e-mail: salama_hady@cic-cairo.com

Electric Charge:

Electric charge was defined, according to a previously introduced entropy-approach [1], as a form of energy or electromagnetic waves that have an electric potential, positive or negative. So; the unit of electric charge is a unit of Energy, i.e. in Joules. Hence; the current as a rate of flow of electric charge should be measured in Watt. Accordingly; the ammeter does not read such defined current but reads actually the rate of flow of electric energy per Volt. This can be shown from the following well known equation that is used in electric- power measurement or calculation [2]:

(W_e ) ̇= A * V …. (1)

Where A can be defined as the ammeter reading and V is the potential difference.

Hence; the units of the Ammeter readings should be:

A= W ̇/V…. (Watt )/Volt (2)

So; the universal system of units, that was previously introduced [3], may use the same ammeter as an instrument for measuring the current in Watt/Volt. The Ammeter does not measure actually the rate of flow of electric energy as previously assumed in Coulomb/sec but it measures the flow of electric entropy associated by the electric energy [3].

Magnetic Flux:

Magnetic Flux is defined also according to a published entropy approach and experimental work as a form of energy or electromagnetic waves that have magnetic potential, positive or negative [1]. So; the magnetic flux has to be measured in the same units of energy; i.e. in Joule. According to a scientific analogy between thermal, electric and magnetic energies and their common effect on an Al-Fe thermocouple [3]; it was found that their potentials could be measured also by the Volt. Revising the techniques of measurement of the magnetic flux; it is found that they depend on measuring the produced electric potential by the influence of the measured magnetic field on a conductor that carries an electric current [4]. So; the techniques used do not follow a direct approach but they depend on measuring electric-field parameters to find the corresponding magnetic parameters.

However; we can measure directly the magnetic energy that performs work in attracting iron balls along an inclined plane [1]. Hence; it is possible to recalibrate the already used Gauss-meter to measure the rate of flow of magnetic flux during such attraction process. According to the proved analogy between electric and magnetic fields and the common unit of their potentials as previously described; it is possible to assume the unit of measurement of the modified Gauss-meter to be identical to the unit of Ammeter readings; i.e. in Watt/volt. So; we may introduce the following equation to measure or calculate the magnetic power from readings of the Gauss-meter by an equation that is analogous to equation (1):

(W_m ) ̇ =G*H (3)

Where G is the Gauss-meter reading and H is the magnetic potential in Volt. Hence; the unit of measurement in a modified Gauss-meter for measuring the rate of flow of magnetic flux per unit magnetic potential will be, according to equation (3), as follows:

G = W ̇/V…. (Watt )/Volt (4)

By analogy; this unit measures the rate of flow of magnetic entropy associated by the magnetic energy [3].

References:

[1] Abdelhady, S., “A Fundamental Equation of Thermodynamics that Embraces Electrical and Magnetic Potentials” J. Electromagnetic Analysis & Applications”, March, 2010, Vol. 2: pp. 162- 168.

[2] Jewett, Jr., Serway, R. A., “Physics for Scientists and Engineers with Modern Physics,” 7th Ed., Thomson, Brooks/Cole, 2008.

[3] Abdelhady, S., “ An Approach to a Universal System of Units“J. Electromagnetic Analysis & Applications”, March, 2010, Vol. 2: pp. 162- 168.

[4] Gordon, D. Brown, R. Haben, J., “Methods for measuring the magnetic field,” Magnetics, research Transactions, vol.8/1, pp. 48-51.

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