Physics And Measurement Question 257

Question: If electronic charge e, electron mass m, speed of light in vacuum c and Planck’s constant h are taken as fundamental quantities, the permeability of vacuum $ {\mu _{0}} $ can be expressed in units of

Options:

A) $ ( \frac{h}{me^{2}} ) $

B) $ ( \frac{hc}{me^{2}} ) $

C) $ ( \frac{h}{ce^{2}} ) $

D) $ ( \frac{mc^{2}}{he^{2}} ) $

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let $ {\mu _{0}} $ related with e, m, c and h as follows. $ {\mu _{0}}=ke^{a}m^{b}c^{c}h^{d} $

$ [ML{{T}^{-2}}{{A}^{-2}}]={{[AT]}^{a}}{{[M]}^{b}}{{[L{{T}^{-1}}]}^{c}}{{[ML^{2}{{T}^{-1}}]}^{d}} $

$ -[{{M}^{b+d}}{{L}^{c+2d}}{{T}^{a-c-d}}A^{a}] $

On comparing both sides we get $ a=-2,b=0,c=-1,d=1 $

$ \therefore [{\mu _{0}}]-[ \frac{h}{ce^{2}} ] $



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