Part 3. Electrical and Magnetic Units

11

ELECTROSTATIC SYSTEM



Capacitance of an insulated conductor is proportional to the ratio of the

quantity of electricity in a charge to the potential of the charge. The dimensional formula is the ratio of the two formulae for electric quantity and

potential or [M'L:T-lK'/M'L'T-'K-'] or [ L K ] .

Conductance of any part of an electric circuit, not containing a source of

electromotive force, is the ratio of the current flowing through it to the difference of potential between its ends. The dimensional formula is the ratio of the

formulae for current and potential or [M'L;T-2K'/M'L'T'K-i] or [ L T - l K ] .

Electrical conductivity, like the corresponding term for heat, is quantity

per unit area per unit potential gradient per unit of time. The dimensional

formula is [ M ' L g T ' K 4 / L 2 ( M 4 L

*TT-'Ki

/ L ) T ] or [ T ' K ] .

Electric current (statampere-unit quantity) is quantity of electricity flowinn through a cross section per unit of time. The dimensional formula is the

raTio of tKe formulae for electric quantity and for time or [ M * L > P K ' / T or

]

[M3L;T2K'],

Electric field intensity strength at a point is the ratio of the force on a

quantity of electricity at a point to the quantity of electricity. The dimensional

formula is therefore the ratio of the formulae for force and electric quantity or

[ M L T-2/M L 2 T-lK' ] or [ h14L-3 T-lK-' I .

Electric potential difference and electromotive force (emf) (statvoltwork = 1 erg) .-Change of potential is proportional to the work done per unit

of electricity in producing the change. The dimensional formula is the ratio of

the formulae for work and electrical quantity or [ML2Z'2/M'L;T1K4]or

[MiLiT-'K-'].

Electric surface density of an electrical distribution at any point on a surface is the quantity of electricity per unit area. The dimensional formula is the

ratio of the formulae for quantity of electricity and for area or [ M'L-' T ' K ' ] .

Quantity of electricity has the dimensional formula [ M' LZT' K ' ] , as

shown above.

Resistance is the reciprocal of conductance. The dimensional formula is

EL-'TK-'].

Resistivity is the reciprocal of conductivity. The dimensional formula is

[ TK-'1 .

Specific inductive capacity is the ratio of the inductive capacity of the

substance to that of a standard substtnce and therefore is a number.

Exs.-Find the factor for converting quantity of electricity expressed in ft-grain-sec

units to the same expressed in cgs units. The formula is Im*lgt-'k'], in which m=0.0648,

1 = 30.48, t = 1, k = 1 ; the factor is 0.06483 X 30.481, or 42.8.

Find the factor reauired to convert electric ootential from mm-mp-sec units to CPS

units. The formula is [ m ' l * t - l / d ] ,in which m =b.OOl, 1 = 0.1, t = 1, k-= 1 ; the factor is

0.001, x 0.14, or 0.01.

Find the factor required to convert electrostatic capacity from ft-grain-sec and specificinductive capacity 6 units to cgs units. The formula is [Ikl in which I = 30.48, k = 6;

the factor is 30.48 X 6 , or 182.88.

Y



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12

ELECTROMAGNETIC SYSTEM



Many of the magnetic quantities are analogues of certain electric quantities.

The dimensions of such quantities in the electromagnetic system differ from

those of the corresponding electrostatic quantities in the electrostatic system

only in the substitution of permeability p for K.

Conductance is the reciprocal of resistance, and the dimensional formula is

[L-'Tp-11.

Conductivity is the quantity of electricity transmitted per unit area per unit

potential gradient per unit of time. The dimensional formula is [M'L'p-'/

L2(MfLgT-2p.1/L)

TI or [L-*Tp-'].

Current, I (abampere-unit magnetic field, Y = 1 cm), flowing in circle,

radius r, creates magnetic field at its center, 2 ~ l / r .Dimensional formula is

product of formulae for magnetic field intensity and length or [M'L'Fp-'I.

Electric field intensity is the ratio of electric potential or electroinotive

force and length. The dimensional formula is [M'L*T L p ' ] .

E le ctric potential, or electromotive force (emf) (abvolt-work- 1 erg),

as in the electrostatic system, is the ratio of work to quantity of electricity.

The dimensional formula is [ML2T-'/M'L'p-'] or [M'LI T ' p ' ] .

Electrostatic capacity is the ratio of quantity of electricity to difference of

potential. The dimensional formula is [ L-'T2p-'].

I n t e n s i t y of magnetization ( I ) of any portion of a magnetized body is

the ratio of the magnetic moinent of that portion and its volume. The dimensional formula is [MfLgT-1pL1/L3]

or [M'L-'?"'p*].

Magnetic field str e n g t h , magnetic i n t e n s i t y or magnetizing f o r c e ( I )

is the ratio of the force on a magnetic pole placed at the point and the magnetic

pole strength. The dimensional formula is therefore the ratio of the formulae

for a force and magnetic quantity, or [MLT2/M'LzT-'p']or [M*L-'T-'p-*].

Magnetic flux (a) characterizes the magnetized state of a magnetic circuit.

Through a surface enclosing a magnetic pole it is proportional to the magnetic

pole strength. The dimensional formula is that for magnetic pole strength.

Magnetic induction ( B ) is the magnetic flux per unit of area taken perpendicular to the direction of the magnetic flux. The dimensional formula is

[ M'Lz T-'p4/L2]or [M'L -*T-'p'].

Magnetic moment ( M ) is the product of the pole strength by the length of

the magnet. The dimensional formula is [M'LzT'lp.l].

Magnetic pole s t r e n g t h or q u a n t i t y of magnetism

been shown to have the dimensional formula [M'L;T-'p'].



(11%)



has already



Magnetic potential or magnetomotive force at a point is measured by

the work which is required to bring unit quantity of positive magnetism from

zero potential to the point. The dimensional formula is the ratio of the formulae

for work and magnetic quantity [ M L 2 T 2 / X i L ~ T - ' por

* ][M'L'T-'p-*].

Magnetic reluctance is the ratio of magnetic potential difference to magnetic flux. The dimensional formula is [ L ? p - l ] .

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Magnetic susceptibility ( K ) is the ratio of intensity of magnetization

produced and the intensity of the magnetic field producing it. The dimensional

formula is [M'L-'T-'p'/M'L-'T-' P 1 or [PI.



-'



Mutual inductance of two circuits is the electromotive force produced in

one per unit rate of variation of the current in the other. The dimensional

formula is the same as for self-inductance.

Peltier effect, coefficient of, is measured by the ratio of the quantit,ppf

heat and quantity of electricity. The diinensional formula is [ML2T2/M1L p '1

or [M*L~T-'p*],

the same as for electromotive force.

Q u a n t i t y of electricity is the product of the current and time. The diniensional formula is [M'L1p-+].

Resistance of a conductor is the ratio of the difference of potential between its ends and the constant current flowing. The dimensional formula is

[ll,f1L T-?p1/M4L1T-1p -& ] or [ L T - l p ] .

Resistivity is the reciprocal of conductivity as just defined. The dimensional formula is [ L 2 T 1 p ] .

Self-inductance is for any circuit the electromotive force produced in it by

unit rate of variation of the current through it. The dimensional formula is

the product of the formulae for electromotive force and time divided by that

for current or [ M 1 L 8 T 2 p 1 ~ T ~ M ' L ' T - 1 p - or

1] [ L p ] .

Thermoelectric power is measured by the ratio of electromotive force and

temperature. The dimensional formula is [ M'L2T-'pW1].

Exs.-Find the factor required to convert intensity of magnetic field from ft-grain-min

units to cgs units. The formula is [ m ~ / - ~ f - l p;&~n

l = 0.0645, 1 = 30.48, t = 60, and p = 1 ;

the factor is 0.0648: X 30.45-:, or 0.046108.

How many cgs units of magnetic moment make one ft-grain-sec unit of the same quantity? The formula is [ m i l t-'p!I ; 1% = 0.0648. 1 = 30.48, f = 1, and p = 1 ; the number

is 0.06481 x 30.48a, or 1305.6,

If the intensity of magnetization of a steel bar is 700 in cgs units, what will it be in

mm-mg-sec units? The formula is [ ? t z + l ~ f - * p; *m

] = 1000, 1 = 10, t = 1, p = 1 ; the intensity is 700 x 1000' X ,lo', or 70000.

Find the factor required to convert current from cgs units to earth-quadrant-lO-=

gram-sec units. The formula is [ ~ n * l + t - ' p - ;~ Inz = lo", 1 = lo-@,p = 1 ; the factor is

10V x lo-!, or 10.

Find the factor required to convert resistance expressed in cgs units into the same expressed in earth-quadrant-10"' gram-sec units. The formula is [ I t P p l ; I = lo-', t = 1,

p = 1 ; the factor is lo-'.

TABLE 3.-FUNDAMENTAL



Part 1.-Selection



STANDARDS



of fundamental quantities



The choice of the nature of the fundamental quantities already made does

not sufficiently define the system for measurements. Some definite unit or

arbitrarily chosen standard must next be taken for each of the fundamental

quantities. This fundamental standard should hzve the qualities of permanence, reproducibility, and availability and be suitable for accurate measures.

Once chosen and made it is called the primary standard and is generally kept

at some central bureau-for

instance, the International Bureau of Weights

and Measures at Scvres, France. A primary standard may also be chosen and

made for derived units (e.g., the new absolute (1945) ohm standard.), when

it is simply a standard closely representing the unit and accepted for practieal

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14

purposes, its value having been fixed by certain measuring processes. Secondary or reference standards are accurately compared copies, not necessarily

duplicates, of the primaries for use in the work-of standardizing laboratories

and the production of working standards for everyday use.



Standard of length.-The primary standard of length which now almost

universally serves as the basis for physical measurements is the meter. I t is

defined as the distance between two lines at 0" C on a platinum-iridium bar

deposited at the International Eureau of Weights and Measures. This bar is

known as the International Prototype Meter, and its length was derived from

the ''metre des Archives," which was made by Eorda. Borda, Delambre,

Laplace, and others, acting as a committee of the French Academy, recommended that the standard unit of length should be the ten-millionth part of the

length, from the equator to the pole, of the meridian passing through Paris. In

1795 the French Republic passed a decree making this the legal standard of

length, and an arc of the meridian extending from Dunkirk to Barcelona was

measured by Delambre and Mechain for the purpose of realizing the standard.

From the results of that measurement the meter bar was made by Corda. The

meter is now defined as above and not in terms of the meridian length ; hence,

subsequent measures of the length of the meridian have not affected the length

of the meter.

S t a n d a r d of mass.-The primary standard of mass now almost universally

used as the basis for physical measurements is the kilogram. It is defined as

the mass of a certain piece of platinum-iridium deposited at the International

Bureau of Weights and Measures. This standard is known as the International

Prototype Kilogram. Its mass is equal to that of the older standard, the "kilogram des Archives," made by Borda and intended to have the same mass as a

cubic decimeter of distilled water at the temperature of 4" C.

Copies of the International Prototype Meter and Kilogram are possessed by

the various governments and are called National Prototypes.

unit of time universally used is the mean solar

S t a n d a r d of time.-The

second, or the 86400th part of the mean solar day. It is based on the average

time of one rotation of the earth on its axis relatively to the sun as a point of

reference= 1.002 737 91 sidereal second.

S t a n d a r d of temperature.-The standard scale of temperature, adopted by

the International Committee of Weights and Measures ( 1887), depends on

the constant-volume hydrogen thermometer. The hydrogen is taken at an

initial pressure at 0" C of 1 meter of mercury, 0" C, sea-level at latitude 45".

The scale is defined by designating the temperature of melting ice as 0" and of

condensing steam as 100" under standard atmospheric pressure.

Thermodynamic (Kelvin) Scale (Centigrade degrees).-Such

a scale

independent of the properties of any particular substance, and called the

thermodynamic, or absolute scale, was proposed in 1848 by Lord Kelvin. The

temperature is proportional to the average kinetic energy per molecule of a

perfect gas.



International temperature scale.-See



Table 37.



Numerically different systems of units.-The

fundamental physical

quantities which form the basis of a system for measurements have been chosen

and the fundamental standards selected and made. Custom has not however

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