Question

The dimensional formula of magnetic flux is :

• A. $\left[M^1{L}^2{T}^{-1}{A}^{-2}\right]$
• B. $\left[M^1{L}^2{T}^{-2}{A}^{-1}\right]$
• C. $\left[M^1{L}^2{T}^{-1}{A}^{-1}\right]$
• D. $\left[M^1{L}^0{T}^{-2}{A}^{-1}\right]$

Answer 1

The correct option is B $\left[M^1{L}^2{T}^{-2}{A}^{-1}\right]$

The force experienced by a moving charge in a magnetic field is given by $F=q(\overrightarrow{v}\times \overrightarrow{B})$

Here, $\overrightarrow{B}$ is the magnetic field or magnetic flux density or magnetic flux per unit area.

Thus, dimensions of magnetic flux $\left[\Phi \right]=\left[B\right]\times \left[\text{Area}\right]=\frac{\left[F\right]\left[A\right]}{\left[q\right]\left[v\right]}$

We know the dimensions of the following as-

$\left[F\right]=\left[M^1{L}^1{T}^{-2}\right]$

$\left[A\right]=\left[L^2\right]$

$\left[q\right]=\left[A^1{T}^1\right]$

$\left[v\right]=\left[L^1{T}^{-1}\right]$

Thus, $\left[\Phi \right]=\frac{\left[M^1{L}^1{T}^{-2}\right]\left[L^2\right]}{\left[A^1{T}^1\right]\left[L^1{T}^{-1}\right]}=\left[M^1{L}^2{T}^{-2}{A}^{-1}\right]$