Question

The dimensional formula for magnetic moment of a magnet is:
A. $\left[ {{M^0}{L^2}{T^0}{A^1}} \right]$
B. $\left[ {{M^0}{L^2}{T^0}{A^{ - 1}}} \right]$
C. $\left[ {{M^0}{L^{ - 2}}{T^0}{A^{ - 1}}} \right]$
D. $\left[ {{M^1}{L^{ - 2}}{T^0}{A^{ - 1}}} \right]$

Answer 1

Hint: The magnetic moment of a magnet is a quantity that determines the torques, it will experience in an external magnetic field. A loop of electric current, a bar magnet, on an electron revolving around a nucleus, a molecule and a plant all have magnetic moments.

Complete step by step solution:
he magnetic moment for a current carrying loop is given as $M = IA......\left( i \right)$
Taking of with the side of equation (i)
Unit of M$ = $unit of (IA)
Or, unit of M $ = $unit of (I) $ \times $unit of (A)
$ = $ $ampere \times \,metr{e^2}$
Putting the dimension of these units,
Dimension of \[M = A \times {L^2}\]

Therefore, option A is correct.

Note:

Fundamental physical quantities	Fundamental units of these physical quantities	Dimension of these fundamental quantities
Mass	Kilogram	\[\left[ M \right]\]
Length	Meter	\[\left[ L \right]\]
Time	Second	\[\left[ T \right]\]
Electric current	Ampere	\[\left[ A \right]\]
Temperature	Kelvin	$\left[ \theta \right]$
Luminous intensity	Candela	$\left[ {cd} \right]$
Amount of substance	Mole	$\left[ {mol} \right]$