There is another useful system of units, besides the SI/MKS. A system called the CGS (Centimeter-Gram-Second) system. In this system, Coulomb's law is given by
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 1 es units of charge. The number [3] actually arises from the speed of light in the vacuum which is now taken to be exactly given by . An approximate value of c then is .
(i) Show that Coulomb's law in CGS units yields 1 esu of charge 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 = x C, where x is a dimensionless number. Show that this gives with , we have
Hint: Use Coulomb's law.
(i) Step 1: Find the dimensions of esu.
From the relation,
So, 1 esu of charge
Thus, esu of charge is represented in terms of fractional powers of M and of L.
(ii) Step 2: Put the value of charges in esu.
Let 1 esu of charge = x C, where x is a dimensionless number. Coulomb force on two charges, each of magnitude 1 esu separated by 1 cm is dyne. This situation is equivalent to two charges of magnitude xC separated by
Taking, , we get,
If , we get, .
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