Question

The dimensional formula for magnetic moment is :
(A) \[\left[ {{M^0}{L^2}{T^0}{A^1}} \right]\]
(B) \[\left[ {{M^0}{L^1}{T^0}{A^2}} \right]\]
(C) \[\left[ {{M^0}{L^2}{T^0}{A^2}} \right]\]
(D) \[\left[ {{M^0}{L^0}{T^1}{A^1}} \right]\]

Answer 1

Hint: Dimension formula is the expression for the unit of a physical quantity for the wait of a physical quantity in terms of the fundamental quantities. The fundamental quantities are mass (M) Length (L) and Time (T). A dimension formula is expressed in terms of power of M, L and T.

Complete step by step solution:
 While solving questions related to fundamental dimensional formula which about writing the given physical quantity in terms of other physical quantities whose dimensional formula is known.

The magnitude of magnetic moment to a closed loop is proportional to
Current \[\left[ {{M^0}{L^0}{T^0}{A^1}} \right]\]
Area of Loop \[\left[ {{M^0}{L^2}{T^0}{A^0}} \right]\]

Therefore the dimensional formula for magnetic moment = \[\left[ {{M^0}{L^2}{T^0}{A^1}} \right]\]

Note: We can find any kind of dimensional formula by knowing the formula of particular topic
For eg. - \[ \to Speed = Dis\tan ce = \dfrac{1}{T}\]
Dimensional formula = \[\left[ {L{T^{ - 1}}} \right]\]