Electromagnetic Units

The path to the SI units has been arduous. Being an engineer for many years, I know some of it's history.

Totally independent definitions for the statcoulomb (In 1785 C.A.Coulomb established the statcoulomb "ElectroStaticUnit" of charge.) and the abampere were originally created, without knowledge of how one effected the other. The statcoulomb; by attraction or repulsion of one dyne, of a set charge, one cm apart. The abampere; by attraction or repulsion of one dyne of set current, of one pi of a one cm radius loop, one cm apart.

The abampere is current made up of charge; the same charge as the statcoulomb. The only difference is the abampere is abcoulombs/sec. In other words the charge is moving! So we have two different fields, the electrostatic, and the magnetic; producing each a force of one dyne, and each composed of charge. In either case, the charge is defined as a measure that produces so much force: one dyne. But how are these two charges related? Which is more? Are they equal?

You can send a static charge around a loop just as easily as a current from a battery source. In either case, the current is made of electrons. Static electrons (sitting still) produce a known force of one dyne. How much force would be produced from those same electrons as moving electrons? Here is where that capacitor, that I introduced in the electrostatic section, comes in. A capacitor stores charge. But the capacitors in those days were very small, measured in picofarads. The success comes with finding a large cap. As the electrostatic balls were charged, the cap was charged too. It took longer for the balls to reach the q for the one dyne force. But with the cap, a pulse volt meter could successfully read the abvoltage.
EqCAPQ.gif, 2 kB
Switching over to the magnetic apparatus, we have coils of hundreds of turns, and we know the voltage that produced the calibrated abcoulomb/sec definition. When the calculations were finished, it was discovered that the abcoulomb was a HUGE amount bigger than the statcoulomb. Finer calculations gave a value of abcoulomb = 3E10 statcoulombs.
EqABSTAT.gif, 4 kB

Now here is where the naming conventions get crazy...
"Ego-wars" broke out between the "electrostatic guys", and the newly emerging "electrical guys": Which system of measurement was better! No body settled down long enough to take a closer look at that transformation constant. That constant is actually "c" the speed of light!!! Instead, the electrical guys tried to eliminate it - and to jack around values to suit values of their batteries. First they reduced the abamp by 10 because they thought it was to high for their practical work (and counting ability). Today, one abampere (cgs system) is equal to ten amperes in the SI system of units. So now that beautiful constant "c" was changed down to 3E9.
EqPRACTAMP.gif, 2 kB
They should have been taken out and shot! I hope they rot in their graves! The tragedy took hold, and it was too late to change it back.

But they were not done...
The idiots decided that they wanted to change the volt too! My understanding is that the electrical "engineers" had lead-acid batteries that they thought the world of. They wanted a voltage between 0 and 10 to represent their battery voltage. I am starting to get sick.

With total disregard to that magical number "c", they decided that the statvolt was too small, and the abvolt too big. They decided to make their "practical" volt 1/300 of a statvolt. EqPRACTVOLT.gif, 2 kB

There is more to the story, but I have to go to the bathroom...

The problem is rather like cutting the pealing off an apple to remove the dirt. Pioneers have liberties to remove constants - at least to adjust them. But in removing the pealing, one removes most of the vitamins. One must not remove "variables", they are essential for the beauty and essence of any equation. The bungling pioneers could not decide if the velocity of light was part of a constant or a variable.

After the dust settled, the modern SI system adopted the "practical" volt and amp, with all the established biases and baggage. But at least the decisiveness has fused a coherent and workable system. Equations MUST have dimensional homogenity.


Magnetic Constant

Eqnu.GIF, 2 kB Eqnumagconst.gif, 2 kB EqnuNA.gif, 2 kB EqnuHenry.gif, 2 kB Eqnukg.gif, 2 kB

Magnetic Constant

BBALLPUR.GIF, 0 kB Magnetic Constant
Magnetic permeability of free space, u0
Magnetic constant (permeability of vacuum) is exact.
Absolute permeability

Eqnnupi.GIF, 1 kB

MagneticConstant (SI units)

u=1.256637061E-06 ... to as many decimal places as you like.
(Magnetic-constant units are: m*kg/s2/A2 , H/m, T*m/A), N/A^2

Fundamental Base units:N/A2 = (meter/sec2)* mass (amp-2) = Newtons per square Amp
Fundamental Base units for "practical": R+1 L-1 T = Ohms/Henry Secs

Relative permeability:
Rationalized: H/m (= Henry/meter)
where Henry is weber/amp-turn
Permanence is webers per ampere-turn
Relative permeability is henries per meter
and is always subject to emperical measurements.

The MagneticConstant is an exact constant; and a defined constant; needs no empirical determination.

Dont't confuse relative permeability u with free space Magnetic constant; the former is dimensionless. The two may be used together like this Equu.gif, 1 kB When the two are taken together, they are stated as simply: "permeability"
Equuu.gif, 1 kB


Electric Constant

Eqnec1.gif, 1 kB
EqUnite.gif, 1 kB

Electric Constant

Electric Constant:
Electric permittivity of free space e0
Also - as well as the magnetic constant - an exact constant and a defined constant; Needs no empirical determination.

Eqnec.GIF, 2 kB

Electric Constant

e in terms of u. (si units)
units: F/m, farad/meter.
units: M-1 L-3 T+2 Q+2

e=8.854187817E-12 as many decimal places as you like.
Units: Newtons/meter


Speed of Light

Eqnc.GIF, 1 kB

Light (in vacuum)

Speed of light c

EqMAXWELL1.gif, 2 kB
EqMAXWELL2.gif, 2 kB
EqMAXWELL3.gif, 2 kB
EqMAXWELL4A.gif, 3 kB
EqMAXWELL4B.gif, 3 kB
InductionLogo.GIF, 4 kB Maxwell4Logo.GIF, 4 kB
(T) A unit of magnetic-force.
The magnetic flux density of a uniform field
that produces a torque of one newton-meter on a plane current loop
carrying one ampere
and having a projected area of one square meter on the plane perpendicular to the field.
T = N/(A m), Tesla units are Newtons per Amp-meter

(T) A unit of magnetic flux density.
Magnetic field strength
A magnetic density of one line
per square meter area, placed normal to field.
Tesla units are Webers per square meter, T = Wb m-2

(T) A unit of magnetic-force.
A particle passing through a magnetic field of one Tesla
at one meter per second
carrying a charge of one Coulomb
experiences a force of one Newton
T = (N s)/(Q m)
Tesla units are Newton seconds per Coulomb per meter
T = N/(A m), Tesla units are Newtons per Amp-meter

(T) A unit of magnetic induction.
kg/(A s2), kilogram per amp per second squared
kg/(C s), kilogram per Coulomb per second
One Tesla is equal to 1 Newton/(A/m).
One Tesla is equal to 1 Newton/(H).

(Wb) A unit of magnetic flux.
The magnetic flux passing through an area of one square meter
placed normal to a uniform magnetic field
of magnetic flux density equal to 1 tesla.
Wb = T m^2.
Weber units are Telsas times their square meters.

If the flux linked by a circuit changes at a uniform rate of 1 weber per second,
a voltage of 1 volt is induced in the circuit.
Wb = V s
Weber units are volt seconds.