Three is another useful system of units, besides the SI/mksA system, called the cgs (centimeter-gram -second) system, Coulumb's law is givenby F = (Qq)/(r^(2)) hat(r ) 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), where1 esunit of charge =(1)/([3]) xx 10^(-9) C The number [3] actually ariesfrom the speed of light in vacumm which is now taken to be exactly given by c = 2.99792458xx10^(8) m//s. An approximatevalue of c thenis c = [3] xx10^(8) m//s. (i) Show that the coulomb law in cgs units yields 1 esu of charge = 1 (dyn e)^(1//2)cm. Obtain the dimensious of units of charge in terms of mass M, length L and time T. Show that it is given in termsof fractional powers of M and L. (ii) Write 1 esu of charge = xC, wherex is a dimenionless number. Show that this gives (1)/(4pi in_(0)) = (10^(-9))/(x^(2)) (N.m^(2))/(C^(2)) Withx = (1)/([3]) xx10^(-9), we have (1)/(4pi in_(0)) = [3]^(2) xx10^(9) (Nm^(2))/(C^(2)) or (1)/(4pi in_(0)) = (2.99792458)^(2) xx 10^(9) (Nm^(2))/(C^(2)) (exactly).