Question

An electron of charge $e$ and mass $m$ is moving in circular path of radius $r$ with a uniform angular speed $\omega$. Then which of the following statements are correct ?

• A. The equivalent current flowing in the circular path is proportional to $r^2$
• B. The magnetic moment due to circular current loop is independent of $m$
• C. The magnetic moment due to circular current loop is equal to $2e/m$ time the angular momentum of the electron
• D. The angular momentum of the particle is proportional to the areal velocity of electron.

Answer 1

The Correct Option is D

Magnetic moment, $m=l A$
$=\frac{e V}{2 \pi r} \times \pi r^{2}=\frac{e v r}{2} $
Angular momentum $=2 m \frac{d A}{d t}$

Answer 2

Magnetic Dipole Moment

The magnetic moment of a magnet, or any other object that generates a magnetic field, is its strength and direction. 

• It is also known as the magnetic dipole moment of an object. 
• The magnetic dipole moment quantifies a dipole's capacity to align with the external magnetic field.

The magnetic dipole moment is calculated by multiplying the pole strength of each pole by the distance between the magnetic poles.

M = q_m x 2l

Where

• M is magnetic dipole moment
• q_m is the pole strength
• 2l is the distance between the poles

It is a vector quantity and its direction is from south to north pole.

The pole strength of a magnetic dipole of a magnet is determined by the area of the magnetic dipole's cross-section.

• When a bar magnet is divided horizontally into two equal halves, the pole strength of each portion is reduced to half, and the dipole moment of each component is half of its original value.
• When a bar magnet is divided vertically into two equal parts, the pole strength of each pole stays constant, but the magnetic length is reduced to half, and the dipole moment of each portion is decreased to half of its original value.