JOURNAL 1, ELECTROMAGNETIC THEORY 2, 13.0.0.3.0
1
Dimensional analysis of Maxwell’s equations Lennin G´ Galvez, a´ lvez, Escuela de Mec´ anica El´ ectrica USAC
Abstract—To understand the nature in its more fundamental form and behavior we need have awareness of its fundamental properties and its behavior, electricity and magnetism is one of the more more powerf powerfull ull phe phenom nomeno enon n in the univer universe se then then let’s let’s to fumigar.
4) The charge charge density: density:
ρv =
Colulumb per cubic meters, electric charge per volume. 5) The differenti differential al cubic cubic volume: volume:
I. I NTRODUCTION
A
QUANTITY in the genaral sense is a property ascribed to phenomena, bodies, or substance like a mass and electric charge. A quan quanti tity ty in the the part partic icul ular ar sens sensee is a quan quanti tifia fiabl blee or assignable property ascribed to a particular phenomenon, body, or substance like the mass of the moon and the electric charge of the proton. A physical quantity is a quantity that can be used in the mathematical equations of the science and technology. A unit is a particular physical quantity, defined and adopted by convent convention, ion, with which which other other particul particular ar quantiti quantities es of the same kind are compared to express their value. The value value of a physic physical al quanti quantity ty is the quanti quantitat tativ ivee exexpression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. thus, the numerial value of a particular physical quantity depends on the unit in which it is expressed. 13.0.0.3.0 19-02-2013
dv = m 3 Volume. B. Gauss’ law for magnetic field
B · ds = 0
s
1) Magnetic Magnetic flux density: density:
B=
· 0 E ds ·
=
s
kg Cs
Mass per coulomb times seconds, mass, electric charge, and time. C. Faraday’ araday’ss law of induction induction
d E · · dl = − dt l
I I . I NTEGRAL FORMS OF M AXWELL’ S EQUATIONS A. Gauss’ law for electric field
C m3
B · ds
s
1) Diefferential Diefferential length:
dl = m ρv dv
v
Length
1) Electrical permitivity permitivity for hipothetical space:
0 =
C 2 s2 m3 kg
Electric charge squared times second squared, per mass times cubic meters. Electric charge, time, length, and mass. 2) Electric Electric field: field: mkg E = C s2 Kilogram times meter per coulomb times second squared. Mass, length, electric charge, and time. 3) The differential differential surface:
ds = m 2 Length times length, a flat differential surface.
D. Ampere Maxwell law
B l
∂ · dl = J ds + · · µ0 ∂t s
· 0 E ds ·
s
1) Magnetic permeability permeability for hipothetical space:
µ0 =
kgm kg m C 2
Mass, length, and electric charge. 2) The current current density: density:
J =
C sm2
Electric charge, time, and lenght.
JOURNAL 1, ELECTROMAGNETIC THEORY 2, 13.0.0.3.0
III. I NDEX Base quantity length mass time electric − charge, −quantity − of − electricity electric − current area volume speed − velocity acceleration force energy, −work, −quantity − of − heat power, −radiant − flux electric − potential − diference, −electromotive − force capacitance magnetic − flux magnetic − flux − density inductance A PPENDIX A E LECTRIC PERMITIVITY
0 =
F C 1 A C C s C C s C = = = = m V m W m s J m s Nm m C s2 s C C 2 s2 = = s kgm m m kgm3 A PPENDIX B E LECTRIC PERMEABILITY
µ0 =
H Wb 1 Vs 1 W s 1 J s 1 Nm = = = = = m A m A m A Am s A2 m A2 m 2 kgm 1 kgm s kgm = = = 2 2 2 2 s A s C C 2 A PPENDIX C E LECTRIC FIELD
E =
V W J Nm kgm = = = = 2 m Am sAm sAm s Asm kgms kgm = = 2 s Csm s2 C A PPENDIX D M AGNETIC FIELD
B=
Wb Vs Ws Js N ms = = = = 2 2 2 2 m m Am sAm sAm2 kgmms kg kgs kg = = = = 2 2 2 2 s Asm s A s C Cs A PPENDIX E T HE MAGNETIC INTENSITY
H =
B kg C 2 C = = µ0 Cs kgm ms
2
Name-Symbol meter - m kilogram - kg second - s coulomb - C ampere - A square-meter - m2 cubic-meter - m 3 meter-per-second - m s meter-per-second-squared newton - N joule - J watt - W volt - V farad - F weber - W b tesla - T henry - H
m s2
