Question

The dimensions of magnetic flux are?

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

Answer 1

Answer: (D)

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

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

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

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

We know the dimension of the following as,

$\left[F\right]=\left[ML{T}^{-2}\right]$

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

$\left[q\right]=\left[AT\right]$

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

Thus,

$\varphi =\frac{\left[ML{T}^{-2}\right]\left[L^2\right]}{\left[AT\right]\left[L{T}^{-1}\right]}=\left[M{L}^2{T}^{-2}{A}^{-1}\right]$

Option D