Question

The dimensional formula of electric potential is given by

Answer 1

Step 1: Definition and formula of electric potential

Electric potential at a point is the amount of work that has to be done to bring a unit positive charged particle at that point bringing from infinity.

Formula, electric potential, $V=\frac{Workdone}{Charge}=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r}$

Step 2: Calculating the dimensional formula of electric potential

We know, the dimensional formula of work done is $M^1{L}^2{T}^{-2}$

The dimensional formula of charge is $M^0{L}^0{T}^1{A}^1$

Electric potential dimensional formula,

$$\begin{gathered} \left[V\right]=\frac{\left[Workdone\right]}{\left[Charge\right]} \\ \Rightarrow \left[V\right]=\frac{M^1{L}^2{T}^{-2}}{M^0{L}^0{T}^1{A}^1} \\ \Rightarrow \left[V\right]=M^1{L}^2{T}^{-3}{A}^{-1} \end{gathered}$$

Therefore, the dimensional formula of electric potential is $\left[M^1{L}^2{T}^{-3}{A}^{-1}\right]$.