There is another useful system of units, besides the SI/MKS. A system, called the cgs system. In this system Coulumb's law is given by `vecF = (Qq)/(r^2) hatr` where the distance r is measured in cm `(=10^(-2) m)`, F in dynes `(= 10^(-5) N)` and the charges in electrostatic units (es units), where 1es unit of charge = `1/[3] xx 10^(-9) C`. The number [3] actually arises the speed of light in vacuum which now taken to be exactly given by `c = 2.99792458 xx 10^8 m/s`. An approximate value of c then is `c = [3] xx 10^8 m/s`.
Show that the Coulomb law in cgs units yields.
1 esu of charge = 1 `(dy )^(1/2) cm`.
obtain the dimension of units of charge in terms of mass M, length L and time T. show that it is given in terms of fractional powers of M and L.

There is another useful system of units, besides the SI/MKS. A system, called the cgs system. In this system Coulumb's law is given by vecF = (Qq)/(r^2) hatr where the distance r is measured in cm (=10^(-2) m) , F in dynes (= 10^(-5) N) and the charges in electrostatic units (es units), where 1es unit of charge = 1/[3] xx 10^(-9) C . The number [3] actually arises the speed of light in vacuum which now taken to be exactly given by c = 2.99792458 xx 10^8 m/s . An approximate value of c then is c = [3] xx 10^8 m/s . Write 1 esu of charge = x C, where x is a dimensoinless number. Show that this gives 1/(4pi epsilon_0) = (10^(-9)/x^2)(N.m^2)/(C^2) with x = 1/[3] xx 10^(-9) , we have 1/(4pi epsilon_0)= [3]^2 xx 10^9 (Nm^2)/(C^2) or 1/(4pi epsilon_0)= (2.99792458)^2 xx 10^9 (Nm)^2/(C)^2 (exactly).

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