Show that units of 1/sqrt(epsilon_o*mu_o)= ms^(-1) ?

1 Answer
Apr 12, 2017

There are many methods by which we can attempt to show the units of 1/sqrt(epsilon_0 cdotmu_0). Two are as shown below.

epsilon_0 is permittivity of free space and its SI units are farad per meter Fcdotm^-1.
We know that derived unit of farad in SI base units‎ are ‎s^4⋅A^2⋅m^-2⋅kg^-1
As such SI units of permittivity become s^4⋅A^2⋅m^-3⋅kg^-1 .....(1)

Now mu_0 is permeability of free space and its SI units are henry per meter Hcdotm^-1
Reduced to base SI units of henry is kg cdotm^2cdot s^-2cdotA^-2.
As such SI units of permeability become kg cdotmcdot s^-2cdotA^-2 .....(1)

Now we that LHS of equation has units as of
1/sqrt((s^4⋅A^2⋅m^-3⋅kg^-1)(kg cdotmcdot s^-2cdotA^-2))
=>1/sqrt(s^2⋅m^-2)
=>ms^-1
Hence proved.

.-.-.-.-.-.-

We know that by definition

c-=1/sqrt(epsilon_0 cdotmu_0)
where c is velocity of light in vacuum (free space).

Since units of velocity are ms^-1,
:. units of RHS are also ms^-1
Hence proved