Question

The dimensional formula for electric field intensity is:

A.)$\left[ ML{{T}^{-3}}{{A}^{-1}} \right]$
B.)$\left[ ML{{T}^{-1}}{{A}^{-3}} \right]$
C.)$\left[ ML{{T}^{3}}{{A}^{-1}} \right]$
D.)$\left[ ML{{T}^{-3}}{{A}^{1}} \right]$

Answer 1

Hint: The dimensional formula of electric field intensity can be found by using the dimensions of force and charge, as electric field intensity is the force per unit coulomb. Mathematically,

$E=\dfrac{F}{q}$ , where E is electric field intensity, F is the force exerted on charge and q is charge.
So, to obtain a dimension of electric field intensity we will divide the dimension of force and charge.

Complete step by step answer:
Electric field is the region around a charged system where it can exert force on another charged particle. It is represented by Electric field lines. These lines are also called electric lines of forces. The electric field lines are drawn such that the tangent at a point, will give the direction of force at that point. The density of these lines is proportional to the intensity of electric field strength. No two intersect each other because if they do then force would have two different directions at that point.

Dimensional formula of a physical quantity is the expression of it in terms of symbols of fundamental units. It is enclosed in brackets. The fundamental units and their symbols are;
Mass [M] Length [L] Time [T] Current [A] Temperature [K] Amount of substance [mol] Luminous intensity [J]

Electric field intensity of electric field is the force applied by field on unit coulomb charge. , mathematically we can write

$E=\dfrac{F}{q}$

The dimension of force is

$ML{{T}^{-2}}$

The dimension of charge is

${{M}^{0}}{{L}^{0}}{{T}^{1}}{{A}^{1}}$

So, dimension of electric field will be

$ML{{A}^{-1}}{{T}^{-3}}$

Hence the correct option is A.

Note: Electric field intensity is a derived quantity, so its dimension is made from the dimension of base S.I. units. The S.I. base units are also known as fundamental units. Even if the power of dimension of length, time and mass in a physical quantity is zero, it is recommended to mention them.