Question

Three identical thin bar magnets, each of moment M, are placed along three adjacent sides of a regular hexagon as shown in the figure. The resultant magnetic moment of the system is

• (A) M
• (B) M√3
• (C) M√2
• (D) 2M

Answer 1

The Correct Option is D

Explanation:

Resultant of I and II,$M_1=\sqrt{M^2+M^2+2M^2\cos {60}^{\circ }}=\sqrt{3}M$Angle between ${\mathrm{M}}_1$ and ${\mathrm{M}}_{\Vert }$ is ${90}^{\circ }$Hence, the resultant magnetic moment is$M_R=\sqrt{3M^2+M^2+2\sqrt{3}{M}^2\cos {90}^{\circ }}=2M$

Answer 2

A magnetic dipole consists of magnetic poles of equal and opposite strength separated by a small distance. Magnetic needles, bar magnets, current-carrying solenoids, etc. are examples of a magnetic dipole.

Magnetic Dipole Moment

The strength and direction of a magnet, or any other object that creates a magnetic field, are referred to as its magnetic moment. 

• It is also known as an object's magnetic dipole moment. 
• The magnetic dipole moment measures a magnetic dipole's ability to align itself with the external magnetic field.

Mathematically, the product of the pole strength of either pole and the distance between the magnetic poles gives the magnetic dipole moment.

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 depends upon the area of the cross-section of the magnetic

• If a bar magnet is cut horizontally into two equal parts, then the pole strength of each pole reduces to half, and the dipole moment of each part is equal to half of its original value.
• If a bar magnet is cut vertically into two equal parts, then the pole strength of each pole remains the same but the magnetic length is reduced to half, and the dipole moment of each part becomes equal to half of its original value.