Question

Dimensional formula for $\varepsilon_{0}$ is

• A. $\left.M ^{-1} \,L ^{-2} \,A ^{2} \,T ^{2}\right]$
• B. $\left[ ML ^{-2}\, A ^{-2}\, T ^{4}\right]$
• C. $\left[ M ^{-1} \,L ^{-3} \,A ^{2}\, T ^{4}\right]$
• D. $\left[ ML ^{3} \,A ^{-2} \,T ^{-4}\right]$

Answer 1

Answer: (C)

From Coulomb's law, $F=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{1} q_{2}}{r^{2}}$
$\therefore \varepsilon_{0}=\frac{1}{4 \pi F} \frac{q_{1} q_{2}}{r^{2}}$
$\therefore $ Dimensions of $\varepsilon_{0}=\frac{1}{\left[M L T^{-2}\right]} \times \frac{[A T]^{2}}{\left[L^{2}\right]}$
$=\left[M^{-1} L^{-3} T^{4} A^{2}\right]$