There is another useful system of units, besides the SI/mks A system, called the cgs (centimeter-gram-second) system. In this system Coloumb’s law is given by F=Qq/r2 vector 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), where 1es unit of charge=1/[3]x10-9C The number [3] actually arises from the speed of light in vaccum which is now taken to be exactly given by c = 2.99792458 × 108m/s. An approximate value of c then is c = [3] × 108 m/s. (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 = x C, where x is a dimensionless number. Show that this gives

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alok kumar singh | Contributor-Level 10

4 months ago

This is a Long Answer Type Questions as classified in NCERT Exemplar

Explanation- as we know F= Qq/r²= 1dyne = 1esu of charge²/1cm²

1 esu of charge = M^1/2L^3/2T^—1

Q=xC where x is dimensionless quantity

So F= $Q + q_{2} = q_{1}$ =1 dyne = 10^-5N

Taking x= 1/3 $Q = q_{1} - q_{2}$ ⁹

After solving we get 1/4 $q_{1} + q_{2}$

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