Question

Using mass $\left(M\right)$, length $\left(L\right)$, time $\left(T\right)$ and electric current $\left(A\right)$ as fundamental quantities the dimensions of permittivity will be

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

Answer 1

The correct option is C $\left[M^{-1}{L}^{-3}{T}^{+4}{A}^2\right]$

Using Coulomb's law, Force $F=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}\Rightarrow {ϵ}_2=\frac{q_1{q}_2}{4\pi F{r}^2}$
So dimension of $\left[{ϵ}_0\right]$$=\frac{[AT{]}^2}{\left[ML{T}^{-2}\right]\left[L^2\right]}=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$