What Determines the Torque and Magnetic Moment in Magnetic Systems?

[pardesi]

when we write $\vec \tau=[\vec \mu, \vec B]$
what is the point or the line about which we are calcuating the torque
Also what is the magnetic moment's expression for a surface current and volume current distribution?

 

[Shooting Star]

The moment of magnetic dipole is independent of the origin. The torque is a pure couple and so it too is independent of the choice of origin.

 

[astrokreng]

The equation \vec \tau=[\vec \mu, \vec B] represents the relationship between torque (\vec \tau), magnetic moment (\vec \mu), and magnetic field (\vec B). The point or line about which we are calculating the torque is the axis of rotation or the point of application of the force. This equation is commonly used in the study of rotational motion of magnetic systems.

The expression for magnetic moment for a surface current distribution is \vec \mu = I \vec A, where I is the current and \vec A is the area of the surface. For a volume current distribution, the expression is \vec \mu = \int_V \vec J \times \vec r dV, where \vec J is the current density and \vec r is the position vector. These expressions represent the strength and direction of the magnetic dipole moment, which is a measure of the extent to which a magnetic system can be influenced by an external magnetic field.