Question

The dimensions of permittivity $\varepsilon_{0}$ are

• A. $A^{2}T^{2}M^{- 1}L^{- 3}$
• B. $A^{2}T^{4}M^{- 1}L^{- 3}$
• C. $A^{- 2}T^{- 4}ML^{3}$
• D. $A^{2}T^{- 4}M^{- 1}L^{- 3}$

Answer 1

Answer: (B)

$A^{2}T^{4}M^{- 1}L^{- 3}$

Answer 2

$F = \frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}$

$\Rightarrow$ $\varepsilon_{0} = \frac{|q_{1}||q_{2}|}{\lbrack F\rbrack\lbrack r^{2}\rbrack} = \frac{\lbrack A^{2}T^{2}\rbrack}{\lbrack MLT^{- 2}\rbrack\lbrack L^{2}\rbrack} = \lbrack A^{2}T^{4}M^{- 1}L^{- 3}\rbrack$