There is another useful system of units, besides the SI/mks system, called the cgs (centimetre-gram-second) system. In this system, Columb's law is given by
where the distance r is measured in , F in dynes
and the charges in electrostatic units (es units), where 1es unit of charge
The number [3] actually arises from the speed of light in vaccum which is now taken to be exactly given by . An approximate value of c then is
(i) Show that the coloumb law in cgs units yields
1 esu of charge = 1 (dyne)1/2 cm.
Obtain the dimensions 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.
(ii) Write 1 esu of charge where x is a dimensionless number. Show that this gives
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So, 1 esu of charge
Thus the charge in C.G.S. unit (in esu) is represented in terms of fractional power 1/2 of M and 3/2 of L.
Let 1 esu of charge =x C, where x is a dimensionless number. We can consider a situation, two charges of magnitude x C separated by
The force between the charge
Taking,