Question

What is the dimensional formula for electric field intensity?
$
  {\text{A}}{\text{. }}\left[ {{\text{ML}}{{\text{T}}^{ - 3}}{{\text{A}}^{ - 1}}} \right] \\
  {\text{B}}{\text{. }}\left[ {{\text{ML}}{{\text{T}}^{ - 1}}{{\text{A}}^{ - 3}}} \right] \\
  {\text{C}}{\text{. }}\left[ {{\text{ML}}{{\text{T}}^3}{{\text{A}}^{ - 1}}} \right] \\
  {\text{D}}{\text{. }}\left[ {{\text{ML}}{{\text{T}}^{ - 3}}{{\text{A}}^1}} \right] \\
 $

Answer 1

Hint- Here, we will proceed by using the formulas for velocity i.e., Velocity = $\dfrac{{{\text{Length}}}}{{{\text{Time}}}}$, for acceleration i.e., Acceleration = $\dfrac{{{\text{Velocity}}}}{{{\text{Time}}}}$, for force i.e., Force = (Mass)$ \times $(Acceleration), for current i.e., Current = $\dfrac{{{\text{Magnitude of charge}}}}{{{\text{Time}}}}$ and for electric field intensity i.e., Electric field intensity = $\dfrac{{{\text{Force experienced}}}}{{{\text{Magnitude of charge}}}}$.

Complete step-by-step answer:
There are total seven fundamental quantities which exists and these are length whose dimension is denoted by [L], mass whose dimension is denoted by [M], time whose dimension is denoted by [T], temperature whose dimension is [K], electric current whose dimension is denoted by [A], luminous intensity whose dimension is denoted by [Cd] and amount of substance whose dimension is denoted by [mol].
All the other physical quantities (or their dimensions) can be represented in terms of these seven fundamental quantities (or their dimensions).
Since, Velocity = $\dfrac{{{\text{Length}}}}{{{\text{Time}}}}$
So, the dimension of velocity will be $\left[ {{\text{L}}{{\text{T}}^{ - 1}}} \right]$
Also, Acceleration = $\dfrac{{{\text{Velocity}}}}{{{\text{Time}}}}$
So, the dimension of acceleration will be $\left[ {{\text{L}}{{\text{T}}^{ - 2}}} \right]$
Also, Force = (Mass)$ \times $(Acceleration)
So, the dimension of force experienced will be given as $\left[ {{\text{ML}}{{\text{T}}^{ - 2}}} \right]$
Also, Current = $\dfrac{{{\text{Magnitude of charge}}}}{{{\text{Time}}}}$
$ \Rightarrow $Magnitude of charge = (Current)$ \times $(Time)
So, the dimension of magnitude of charge will be $\left[ {{\text{AT}}} \right]$
Also, Electric field intensity = $\dfrac{{{\text{Force experienced}}}}{{{\text{Magnitude of charge}}}}$
So, the dimension of electric field intensity is given as $\dfrac{{\left[ {{\text{ML}}{{\text{T}}^{ - 2}}} \right]}}{{\left[ {{\text{AT}}} \right]}} = \left[ {{\text{ML}}{{\text{T}}^{ - 3}}{{\text{A}}^{-1}}} \right]$
Hence, option A is correct.

Note- In this particular problem, we have converted all the terms used in the formula for Electric field intensity = $\dfrac{{{\text{Force experienced}}}}{{{\text{Magnitude of charge}}}}$ in terms of the seven fundamental physical quantities because the dimensions of any physical quantity is given in terms of the dimensions of these fundamental quantities.