# 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  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

Acording to relation,

So, 1 esu of charge

Hence, [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.

If two charge each of magnitude 1 esu separated by 1 cm, Coulomb force on the charge is 1 dyne =
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,

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