The dimensions of permittivity $ \varepsilon_{0} $ are: [PMT/NEET-1997]
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. $A^{2}T^{-4}M^{-1}L^{-3}$

Solution
Coulomb’s law:
$
F = \frac{1}{4\pi \varepsilon_0} \frac{q_1 q_2}{r^2}
$

So,
$
\varepsilon_0 = \frac{q^2}{F r^2}
$

Dimensions:

• $q = AT$
• $F = MLT^{-2}$
• $r = L$

$
[\varepsilon_0] = \frac{(AT)^{2}}{(MLT^{-2})(L^{2})} = \frac{A^{2}T^{2}}{ML^{3}T^{-2}} = A^{2}T^{4}M^{-1}L^{-3}
$

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