Multiple Choice

Let $$[\varepsilon_o]$$ denote the dimensional formula of the permittivity of the vacuum, and $$[\mu_o]$$ that of the permeability of the vacuum. If M$$=$$mass, L$$=$$length, T$$=$$time and I$$=$$ electric current.

A$$[\mu_o]=M^{-1}L^{-3}T^2I$$
B$$[\varepsilon_o]=M^{-1}L^{-3}T^4I^2$$
Correct Answer
C$$[\mu_o]=MLT^{-2}I^{-2}$$
Correct Answer
D$$[\mu_o]=ML^2T^{-1}I$$

Solution

Dimension formula of ε0
ε0=
1
4πF

v1v2
r2

(F=MLT−2)ε0=
1
MLT−2

LAT×AT
l2

=M−1L−3t4A2
Dimension of μ0
N/A2 or WbA−1m−1=[M][L][T]−2[A]−2

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