Question

Define magnetic moment. Write its S.I. unit and dimension.

Hint:

The easiest way to remember the unit and dimension of magnetic moment is to use the formula for a current loop: \(m = IA\). The units (A and m\(^2\)) and dimensions ([A] and [L\(^2\)]) follow directly from this simple definition.

Answer 1

Step 1: Understanding the Concept:
Just as electric charges create electric fields, moving charges (currents) or intrinsic properties of particles (like electron spin) create magnetic fields. The magnetic moment is the fundamental quantity that characterizes the source of this magnetic field. It determines the torque the object will experience in an external magnetic field.
Step 2: Detailed Definition:
The magnetic dipole moment, often simply called magnetic moment (symbol \(\vec{m}\) or \(\vec{\mu}\)), quantifies the magnetic strength of a dipole.
- For a Bar Magnet: It is a vector that points from the south pole to the north pole of the magnet. Its magnitude is the product of the pole strength and the magnetic length.
- For a Current Loop: A planar loop of wire carrying a current \(I\) with an enclosed area \(A\) has a magnetic moment with magnitude \(m = IA\). The direction of the magnetic moment vector \(\vec{m}\) is perpendicular to the plane of the loop, given by the right-hand grip rule (if you curl the fingers of your right hand in the direction of the current, your thumb points in the direction of \(\vec{m}\)).
The torque \(\vec{\tau}\) experienced by an object with magnetic moment \(\vec{m}\) in an external magnetic field \(\vec{B}\) is given by \(\vec{\tau} = \vec{m} \times \vec{B}\).
Step 3: S.I. Unit and Dimension:
S.I. Unit:
Using the formula for a current loop, \(m = I \times A\):
- The S.I. unit of current (\(I\)) is Ampere (A).
- The S.I. unit of area (\(A\)) is meter squared (m\(^2\)).
Therefore, the S.I. unit of magnetic moment is Ampere-meter squared (A m\(^2\)).
An equivalent unit is Joules per Tesla (J/T).
Dimension:
- The dimension of current (\(I\)) is [A].
- The dimension of area (\(A\)) is [L\(^2\)].
Therefore, the dimensional formula for magnetic moment is [L\(^2\)A].
Step 4: Final Answer:
The magnetic moment is a measure of an object's magnetic properties. Its S.I. unit is A m\(^2\) and its dimension is [L\(^2\)A].