Question: Why do electromagnetism formulas need to be adjusted in the cgs system?
About the article "Electromagnetism", section "Quantities and units".

Candidate passages:
Gaussian units comprise a metric system of physical units.
This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units.
It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units.
The term "cgs units" is ambiguous and therefore to be avoided if possible: cgs contains within it several conflicting sets of electromagnetism units, not just Gaussian units, as described below.
The most common alternative to Gaussian units are SI units.
SI units are predominant in most fields, and continue to increase in popularity at the expense of Gaussian units.
(Other alternative unit systems also exist, as discussed below.)
Conversions between Gaussian units and SI units are not as simple as normal unit conversions.
For example, the "formulas" for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses.
As another example, quantities that are dimensionless (loosely "unitless") in one system may have dimension in another. 
Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere.
The units are:
ampere (electric current)
coulomb (electric charge)
farad (capacitance)
henry (inductance)
ohm (resistance)
tesla (magnetic flux density)
volt (electric potential)
watt (power)
weber (magnetic flux)
In the electromagnetic cgs system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity.
As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.
Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses.
This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units.
Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian, "ESU", "EMU", and Heaviside–Lorentz.
Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units.
The centimetre–gram–second system (abbreviated CGS or cgs) is a variant of the metric system of physical units based on centimeter as the unit of length, gram as a unit of mass, and second as a unit of time.
All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism.
The CGS system has been largely supplanted by the MKS system, based on meter, kilogram, and second.
MKS was in turn extended and replaced by the International System of Units (SI).
The latter adopts the three base units of MKS, plus the ampere, mole, candela and kelvin.
In many fields of science and engineering, SI is the only system of units in use.
However, there remain certain subfields where CGS is prevalent.
In measurements of purely mechanical systems (involving units of length, mass, force, energy, pressure, and so on), the differences between CGS and SI are straightforward and rather trivial; the unit-conversion factors are all powers of 10 arising from the relations and .
For example, the CGS-derived unit of force is the dyne, equal to , while the SI-derived unit of force is the newton, .
Thus it is straightforward to show that .
On the other hand, in measurements of electromagnetic phenomena (involving units of charge, electric and magnetic fields, voltage, and so on), converting between CGS and SI is much more subtle and involved.
In fact, formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on which system of units one uses.
This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units.
Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian, "ESU", "EMU", and Heaviside–Lorentz.
Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units. 
The unit for magnetic moment is not a base unit in the International System of Units (SI).
As the torque is measured in newton-meters and the magnetic field in teslas, so the magnetic moment is measured in newton-meters per tesla (N⋅m⋅T−1).
This is equivalent to ampere-square meters (A⋅m2) and to joules per tesla (J⋅T−1): 1 A·m2 = 1 N·m·T−1 = 1 J·T−1.
In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, Gaussian, and EMU.
Among these, there are two alternative (non-equivalent) units of magnetic dipole moment in CGS:  (ESU CGS) 1 stat A·cm2 = 3.33564095 × 10−14 A·m2 (or N·m·T−1) and  (EMU CGS and Gaussian-CGS) 1 erg/G = 1 abA·cm2 = 10−3 (m2·A or J/T).
The ratio of these two non-equivalent CGS units (EMU/ESU) is equal to the speed of light in free space, expressed in cm·s−1.
All formulas in this article are correct in SI units, but in other unit systems, the formulas may need to be changed.
For example, in SI units, a loop of current with current I and area A has magnetic moment I×A (see below), but in Gaussian units the magnetic moment is I×A/c. 
The table below shows the values of the above constants used in some common CGS subsystems:The constant "b" in SI system is a unit-based scaling factor defined as: formula_32.
Also, note the following correspondence of the above constants to those in Jackson and Leung: :formula_33 :formula_34 :formula_35 :formula_36 In system-independent form, Maxwell's equations can be written as:formula_37Note that of all these variants, only in Gaussian and Heaviside–Lorentz systems formula_38 equals formula_39 rather than 1.
As a result, vectors formula_40 and formula_41 of an electromagnetic wave propagating in vacuum have the same units and are equal in magnitude in these two variants of CGS.