Single Choice

The dimensional formula of magnetic flux is :

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

Solution

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

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

Thus, dimensions of magnetic flux $$[\Phi] = [B]\times [\textrm{Area}] = \displaystyle \frac{[F][A]}{[q][v]}$$
We know the dimensions of the following as-
$$[F] = [M^1 L^1 T^{-2}]$$
$$[A] = [L^2]$$
$$[q] = [A^1 T^1]$$
$$[v] = [L^1T^{-1}]$$

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

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