8.2 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Centimetre–gram–second system of units | 2/5 | https://en.wikipedia.org/wiki/Centimetre–gram–second_system_of_units | reference | science, encyclopedia | 2026-05-05T14:27:48.320562+00:00 | kb-cron |
=== CGS approach to electromagnetic units ===
The laws of electromagnetism (specifically, the four Maxwell's equations) are formulated with fundamentally different assumptions in SI and CGS units. The SI system introduces new units to represent concepts such as electric charge, current, and magnetic flux, while CGS avoids adding new units. Rather, CGS represents all electromagnetic quantities by expressing the laws of electromagnetism in purely mechanical units, without introducing further units beyond the centimetre, gram, and second.
For example, in SI the unit of electric current, the ampere (A), was historically defined such that the magnetic force exerted by two infinitely long, thin, parallel wires 1 metre apart and carrying a current of 1 ampere is exactly 2×10−7 N/m. This definition results in most SI electromagnetic units being consistent (subject to factors of some integer powers of 10) with those of the CGS-EMU system described in further sections. The ampere is a base unit of the SI system, with the same status as the metre, kilogram, and second. Thus the relationship in the definition of the ampere with the metre and newton is disregarded, and the ampere is not treated as dimensionally equivalent to any combination of other base units. As a result, electromagnetic laws in SI require an additional constant of proportionality (see Vacuum permeability) to relate electromagnetic units to mechanical units. (This constant of proportionality is derivable directly from the above definition of the ampere.) All other electric and magnetic units are derived from these four base units using the most basic common definitions: for example, electric charge q is defined as current I multiplied by time t,
q
=
I
t
,
{\displaystyle q=I\,t,}
resulting in the unit of electric charge, the coulomb (C), being defined as 1 C = 1 A⋅s.
=== Alternative derivations of CGS units in electromagnetism === Electromagnetic relationships to length, time and mass may be derived by several equally appealing methods. Two of them rely on the forces observed on charges. Two fundamental laws relate (seemingly independently of each other) the electric charge or its rate of change (electric current) to a mechanical quantity such as force. They can be written in system-independent form as follows:
The first is Coulomb's law,
F
=
k
C
q
q
′
d
2
{\displaystyle F=k_{\rm {C}}{\frac {q\,q^{\prime }}{d^{2}}}}
, which describes the electrostatic force F between electric charges
q
{\displaystyle q}
and
q
′
{\displaystyle q^{\prime }}
, separated by distance d. Here
k
C
{\displaystyle k_{\rm {C}}}
is a constant which depends on how exactly the unit of charge is derived from the base units. The second is Ampère's force law,
d
F
d
L
=
2
k
A
I
I
′
d
{\displaystyle {\frac {dF}{dL}}=2k_{\rm {A}}{\frac {I\,I^{\prime }}{d}}}
, which describes the magnetic force F per unit length L between currents I and I′ flowing in two straight parallel wires of infinite length, separated by a distance d that is much greater than the wire diameters. Since
I
=
q
/
t
{\displaystyle I=q/t\,}
and
I
′
=
q
′
/
t
{\displaystyle I^{\prime }=q^{\prime }/t}
, the constant
k
A
{\displaystyle k_{\rm {A}}}
also depends on how the unit of charge is derived from the base units. Maxwell's theory of electromagnetism relates these two laws to each other. It states that the ratio of the proportionality constants
k
C
{\displaystyle k_{\rm {C}}}
and
k
A
{\displaystyle k_{\rm {A}}}
must obey
k
C
/
k
A
=
c
2
{\displaystyle k_{\rm {C}}/k_{\rm {A}}=c^{2}}
, where c is the speed of light in vacuum. Therefore, if one derives the unit of charge from Coulomb's law by setting
k
C
=
1
{\displaystyle k_{\rm {C}}=1}
then Ampère's force law will contain a factor
2
/
c
2
{\displaystyle 2/c^{2}}
. Alternatively, deriving the unit of current, and therefore the unit of charge, from Ampère's force law by setting
k
A
=
1
{\displaystyle k_{\rm {A}}=1}
or
k
A
=
1
/
2
{\displaystyle k_{\rm {A}}=1/2}
, will lead to a constant factor in Coulomb's law. Indeed, both of these mutually exclusive approaches have been practiced by users of the CGS system, leading to the two independent and mutually exclusive branches of CGS, described in the subsections below. However, the freedom of choice in deriving electromagnetic units from the units of length, mass, and time is not limited to the definition of charge. While the electric field can be related to the work performed by it on a moving electric charge, the magnetic force is always perpendicular to the velocity of the moving charge, and thus the work performed by the magnetic field on any charge is always zero. This leads to a choice between two laws of magnetism, each relating magnetic field to mechanical quantities and electric charge:
The first law describes the Lorentz force produced by a magnetic field B on a charge q moving with velocity v:
F
=
α
L
q
v
×
B
.
{\displaystyle \mathbf {F} =\alpha _{\rm {L}}q\;\mathbf {v} \times \mathbf {B} \;.}