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}} ] $
