Question

Dimensions of magnetic field intensity is :

A. $[{{M}^{0}}{{L}^{-1}}{{T}^{0}}{{A}^{1}}]$
B. $[ML{{T}^{-1}}{{A}^{-1}}]$
C. $[M{{L}^{0}}{{T}^{-2}}{{A}^{-1}}]$
D. $[ML{{T}^{-2}}A]$

Answer 1

We are supposed to find the dimensional formula of magnetic field intensity. For that, we have to analyse the definition and the numerical formula of the same. Further, we can deduce the dimensional formula by finding the degree of dependence of a physical quantity on another. The principle of consistency of two expressions can be used to find the equation relating these two quantities.

Formulas used:
$F=BIl$, where $F$ is the force experienced by a wire of length $l$ in a magnetic field $B$ when it carries a current of the value $I$.

Complete step by step answer:
We know that the value of the force experienced by a current carrying wire in a magnetic field is obtained from the formula
$F=BIl$
$\Rightarrow B=\dfrac{F}{Il}$
The dimensional formula for force is $[ML{{T}^{-2}}]$
The dimensional formula for current is $[A]$
The dimensional formula for length is $[L]$
Hence, the dimensional formula for B is
$\dfrac{[ML{{T}^{-2}}]}{{{[A]}^{{}}}[L]}=\dfrac{[M{{T}^{-2}}]}{[A]}=[M{{L}^{0}}{{T}^{-2}}{{A}^{-1}}]$
Therefore, we can represent the dimensional formula of magnetic field intensity is $[M{{L}^{0}}{{T}^{-2}}{{A}^{-1}}]$
Therefore, option C is the correct choice among the four.

Note: Dimensional formula is widely used in many areas. However, there are a few problems along the way. Dimensionless quantities as well as the proportionality constant cannot be determined in this way. It does not apply to trigonometric, logarithmic and exponential functions. When we look at a quantity that is dependent on more than three quantities, this approach will be difficult. In line with all of this, if one side of our equation has addition or subtraction of quantities, this approach is not appropriate.