Question

The dimensional formula of magnetic flux is

Answer 1

Step 1: Definition and equation of magnetic flux

Magnetic flux is the magnetic field times the area it passes through.

Formula of magnetic flux, $\Phi =BA\cos \theta$ where

$B$ is the magnetic field strength

$A$ is the area the magnetic field passes through

$\theta$ is the angle between $B$ and $A$

Step 2: Dimension formula of the given terms and calculation

Dimensional formula of $B$ can be derived from the formula $F=Bil$

where $i$ is current, $F$ is force and $l$ is length of the conductor.

Dimensional formula of $B$,

$$\begin{gathered} \left[B\right]=\frac{\left[F\right]}{\left[i\right]\left[l\right]} \\ \Rightarrow \left[B\right]=\frac{\left[M^1{L}^1{T}^{-2}\right]}{\left[M^0{L}^0{T}^0{A}^1\right]\left[M^0{L}^1{T}^0\right]} \\ \Rightarrow \left[B\right]=M^1{L}^0{T}^{-2}{A}^{-1} \end{gathered}$$

Dimensional formula of $\Phi$ ,

$$\begin{gathered} \left[\varphi \right]=\left[B\right]\left[A\right] \\ \Rightarrow \left[\varphi \right]=\left[M^1{L}^0{T}^{-2}{A}^{-1}\right]\left[M^0{L}^2{T}^0\right] \\ \Rightarrow \left[\varphi \right]=M^1{L}^2{T}^{-2}{A}^{-1} \end{gathered}$$

⇒Thus, the dimensional formula of $\Phi$ is $M^1{L}^2{T}^{-2}{A}^{-1}$.