What is the dimensional formula of magnetic flux?

Concept –

The dimensional formula is defined as the expression of the physical quantity in terms mass (M), length (L), time (T) and ampere(A).

Magnetic flux (ϕ) refers to the number of magnetic field lines (B) passing through a given area (A). Its SI unit is Weber (Wb).

Mathematically it is represented as, 

\(\phi=BA\)

We know that, when a charge particle q enters a magnetic field B with a velocity v, it experiences a force which is equal to -

F = q V B

Here, F is the force of a magnetic field

          q is the charge 

          V is the particle's velocity

\(or, \; B=\frac{F}{q V}\)

Explanation :

Hence 

Dimension of magnetic field is calculate using relation \(B = \frac{F}{{qv}}\)

Dimensional formula of force (F) = [MLT^-2]

Dimensional formula of charge (q) = [AT]

 Dimensional formula of velocity (v) = [LT^-1]

\(B=\frac{[M \; L\; T^{-2}]}{[A \; T][L\; T^{-1}]}\)

∴ The dimensional formula of magnetic field B is [MT^-2A^-1].

\(\phi=BA\)

So the dimensional formula of B = [MT^-2A^-1]

The dimensional formula of area (A)= [L²]

Therefore, the dimensional formula of magnetic flux = [MT-2A-1][L2] = [ML²T^-2A^-1]

∴ The dimension formula of magnetic flux is [ML²T^-2A^-1].