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Question: The Dimensional formula for the electric field is……… \(\begin{aligned} & A.[M{{L}^{2}}{{T}^{-3...

The Dimensional formula for the electric field is………
A.[ML2T−3A−1] B.[ML2T−3A−2] C.[MLT−3A−1] D.[M0L0T0A0] \begin{aligned} & A.[M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}] \\\ & B.[M{{L}^{2}}{{T}^{-3}}{{A}^{-2}}] \\\ & C.[ML{{T}^{-3}}{{A}^{-1}}] \\\ & D.[{{M}^{0}}{{L}^{0}}{{T}^{0}}{{A}^{0}}] \\\ \end{aligned}

Explanation

Solution

HINT: Keep in mind the formula for electric field and the dimensions of each and every constraint involved in the formula where Field=ForceCharge\text{Field}=\dfrac{\text{Force}}{\text{Charge}}. Use the basic dimensions of these constituent quantities to determine the dimensional formula of field.

Complete step by step answer:
In science, dimensional analysis is the analysis of the relationships between quantities by identifying their base quantities. The conversion of units from one dimensional unit to another is often done with the SI units’ system of measurement. Every quantity can be expressed in the terms of the following seven dimensions
Dimension Symbol
Length - L
Mass - M
Time - T
Electric charge - Q
Luminous intensity - C
Temperature - K
Angle - None

An electric field E at a point is defined as the force experienced by a unit charge, if placed at that point.

Therefore, Electric field=Force experiencedCharge\text{Electric field}=\dfrac{\text{Force experienced}}{\text{Charge}}

The options are posed with current as a basic unit dimensional analysis rather than a charge. We know that, electric current is defined as the charge flow per unit time:

current=chargetime\text{current}=\dfrac{\text{charge}}{\text{time}}

The dimensional formula of electric charge in terms of current becomes:

[Q]=[AT][Q]=[AT],A representing current here.

We know that, Force F is mass times acceleration
Therefore,

[F]=[Mass][Acceleration]=[MLT−2][F]=[Mass][Acceleration]=[ML{{T}^{-2}}]

Thus, electric filed dimensions:

 !![!! E !!]!! = !![!! F !!]!! [Q]=[MLT−2][AT]=[MLT−3A−1]\text{ }\\!\\![\\!\\!\text{ E }\\!\\!]\\!\\!\text{ }=\dfrac{\text{ }\\!\\![\\!\\!\text{ F }\\!\\!]\\!\\!\text{ }}{[Q]}=\dfrac{[ML{{T}^{-2}}]}{[AT]}=[ML{{T}^{-3}}{{A}^{-1}}]

Therefore, the Electric Field is dimensionally represented as [MLT−3A−1][ML{{T}^{-3}}{{A}^{-1}}]. Option C is correct.

NOTE: All you need to learn to solve this question is the basic formulas which will surely help you to calculate the dimensions very easily. Learning the dimensions of different quantities is not at all a good idea when compared to learning just the formula of the basic quantities. Just the basic formulae from the definition of a quantity will surely help you to achieve the answer in the most efficient way possible.