Question

Dimensions of magnetic flux density is -
A. ${M^1}{L^0}{T^{ - 1}}{A^{ - 1}}$
B. ${M^1}{L^0}{T^{ - 2}}{A^{ - 1}}$
C. ${M^1}{L^1}{T^{ - 2}}{A^{ - 1}}$
D. ${M^1}{L^0}{T^{ - 1}}{A^{ - 2}}$

Answer 1

The above problem can be resolved by using the concepts and applications of the dimensional formulas. The dimensional formula for the magnetic flux density can be obtained by the mathematical relation for the magnetic flux density. The magnetic flux density is determined by taking the ratio of the magnetic flux and the region's volume taken into consideration. Then the corresponding values are substituted, and the final result is obtained.

Complete step by step answer:
The expression for the magnetic flux density is given as,
$B = \dfrac{\phi }{V}$…… (1)
Here, $\phi$ is the magnetic flux and V is the volume, where the magnetic flux can be calculated.
The dimensional formula for the magnetic flux is $\phi = {M^1}{L^3}{T^{ - 2}}{A^{ - 1}}$.
And, the dimensional formula for the volume is $V = {L^3}$.
On substituting the above values in equation 1 as,

B = \dfrac{\phi }{V}\\\ B = \dfrac{{{M^1}{L^3}{T^{ - 2}}{A^{ - 1}}}}{{{L^3}}}\\\ B = {M^1}{L^0}{T^{ - 2}}{A^{ - 1}} \end{array}$$ Therefore, the dimensions of the magnetic flux density is $${M^1}{L^0}{T^{ - 2}}{A^{ - 1}}$$ and option (B) is correct. **Note:** To resolve the above problem, the concept and fundamentals of magnetic flux density are required to understand in the region of analysis, when the amount of magnetic flux is considered in the direction of the right angle in the magnetic flux context. Moreover, there are significant applications of the dimensional formula that need to be taken under consideration, along with learning of deriving the formulas using the concepts of dimensional formulas.