S.I. versus c.g.s. Units

by Jason Harlow

 

Many people think there is one system called “The Metric System”, but actually there are two.  One is the “Système International” or S.I. system, which is the “real” (upper-case) Metric System, which uses Metres, Kilograms and Seconds for length, mass and time.  For this reason it is sometimes called the MKS system.  The “other” (lower-case) metric system uses centimetres, grams and seconds.  It is most often called the c.g.s. system, and sometimes it is called the Gaussian system or the electrostatic system.  There are other traditional differences in the two systems when measuring charge and electric and magnetic fields, for example.

 

This causes a lot of confusion, so many scientists would like it if the whole world would embrace the S.I. system and get rid of c.g.s. units forever.  Unfortunately, a lot of scientists just don’t want to do this.  One reason is that for historical reasons, there are two ways of developing the theories of electrodynamics, and one uses S.I. units, and the other uses c.g.s.   The equations in S.I. include more constants (such as ε0 and μ0) and often look more messy.  The equations in c.g.s. are somewhat more elegant for theorists, so many textbooks use cgs throughout.

 

Here are some examples of units you may encounter, the relevant facts about them, and how they relate to the S.I. and cgs systems:

 

Force

 

The S.I. unit for force comes from F=ma, and is the Newton or N.  1 N = 1 kg∙m/s2. 

 

The c.g.s. unit for force comes from the same equation and is called the “dyne”, or dyn.  1 dyn = 1 g∙cm/s2. 

 

dynes are a lot smaller than Newtons. 105 dyn = 1 N.


Energy

 

The S.I. unit for energy is the Joule, or J.   1 J = 1 kg∙m2/s2.  Other common units for energy include the electron volt: 1 eV = 1.602×10-19 J, the calorie and the Calorie.  The calorie is a very seldom used unit, 1 calorie = 4.184 J.  When referring to food energy, the Calorie (with an upper-case “C”) is much more common.  A Calorie, or Cal,  is equal to 1000 calories, and is sometimes called a kilocalorie, or kcal.  1 Cal = 1 kcal = 4184 J.

 

The c.g.s. unit for energy is the erg. 1 erg = 1 g∙cm2/s2.  

 

ergs are a lot smaller than Joules; 107 ergs = 1 J.


Pressure

 

The S.I. unit for pressure is Pascal, or Pa. 1 Pa = 1 N/m2.  The Earth’s atmosphere at sea level has a pressure of 1.013×105 Pa.  Other common units for pressure are: 1 torr = 133.3 Pa, 1 bar = 105 Pa, and 1 atm = 1.013×105 Pa.

 

The c.g.s. unit for pressure does not have a special name.  It is dyne/cm2.  The Earth’s atmosphere at sea level has a pressure of 1.013×106 dyn/cm2.

 

1 dyne/cm2 represents 10 times less pressure than a Pascal.  10 dyn/cm2 = 1 Pa.

Viscosity

 

The S.I. unit for η, viscosity, is N∙s/m2. This is often called the Poiseuille, or PI.  (pronounced “pwah-soy”).  Water has a viscosity of 10-3 PI.

 

The c.g.s. unit for viscosity is dyn∙s/cm2.  This is called the poise, or P.  (pronounced “pwahz”).   For some reason it is much more commonly used than PI.   Water has a viscosity of 0.01 P, or one centi-poise, or 1 cP.

 

1 poise represents 10 times less viscosity than Poiseuille.  10 P = 1 PI.  

 

Electric Charge

 

The S.I. unit for electric charge is the Coulomb, or C.  It is the amount of charge delivered by 1 Ampere of current in 1 second.  The size of the Ampere is set so that two long, straight, parallel wires separated by 1 metre, each carrying 1 Ampere of current will produce a force of 1 Newton per 1 metre of length.   The magnitude of the charge of an electron is e=1.602×10-19 C.   Despite the hugeness of the Coulomb, it is a very popular unit.

 

The cgs unit for electric charge is the “electrostatic unit”, or esu.  The size of the esu is set so that the constant in Coulomb’s force law is equal to one.  Therefore, two charges each with charge 1 esu sitting 1 cm apart will feel a force between them of 1 dyne.   The magnitude of the charge of an electron is e=4.8×10-10 esu.

 

Coulombs are much bigger than esu.  1 C = 3×109 esu.   In fact the ratio of esu per Coulomb is numerically equal to the speed of light in decimetres per second.

 

Magnetic Field

 

The S.I. unit for magnetic field is the Tesla, or T.  It comes from the cross-product equation for magnetic force on a moving particle: F = qv × B.  The magnetic field, B, must be in units of force per charge per velocity.  So 1 T = 1 N∙s/(C∙m).

 

In cgs units, the equation for magnetic force looks different.  Instead of qv× B, it is (qv/c) × B.  You have to divide by the speed of light, c.  The unit for magnetic field, B, is called the Gauss, G, where 1 G = 1 dyne/esu.  The Earth’s magnetic field at the surface is about 1 G, which makes it a very popular unit.

 

Tesla’s are bigger than Gauss.  1 T = 104 G.