Magnetic moment
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In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic dipole moment is defined as 
, where a is the vector area of the current loop. The direction of the vector area is given by the right-hand rule.
In the more complicated case of a spinning charged solid, the magnetic dipole moment can be found by the following equation: 
, where dτ = r2sinθdrdθdφ and J is the current density.
The magnetic moment in a magnetic field is a measure of the magnetic flux set up by the gyration of an electric charge in a magnetic field. The moment is negative, indicating it is diamagnetic, and equal to the energy of rotation divided by the magnetic field.
In atomic and nuclear physics, the symbol m represents moment, measured in Bohr magnetons, associated with the intrinsic spin of the particle and with the orbital motion of the particle in a system. Also called magnetic dipole moment.
For a system of charges, the magnetic moment is determined by summing the individual contributions of each charge-mass-radius component.
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[edit] Explanation
Magnetic moment can be explained by a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of magnetic force which weakens with distance. Since magnetic poles come in pairs, their forces interfere with each other because while one pole pulls, the other repels. This interference is greatest when the poles are close to each other i.e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given point in space, therefore depends on two factors: on both the strength p of its poles, and on the distance d separating them. The force is proportional to the product 
, where 
describes the "magnetic moment" or "dipole moment" of the magnet along a distance R and its direction as the angle between R and the axis of the bar magnet.
Any rotating charged object, from quarks to galactic superclusters, has a magnetic moment.
For relation between magnetic moment and magnetization see magnetization.
Magnetism can be created by electric current in loops and coils so any current circulating in a planar loop produces a magnetic moment whose magnitude is equal to the product of the current and the area of the loop. When any charged particle is rotating, it behaves like a current loop with a magnetic moment.
The equation for magnetic moment in the current-carrying loop, carrying current 
and of area vector 
for which the magnitude is given by:
where
is the magnetic moment, a vector measured in ampere–square metres, or equivalently joules per tesla, is the current, a scalar measured in amperes, and is the loop area vector , having as x, y, and z coordinates the area in square metres of the projection of the loop into the yz-, zx-, and xy-planes.
[edit] Magnetic moment in a magnetic field
The magnetic moment of an object is a vector relating the aligning torque in a magnetic field experienced by the object to the field vector itself. The relationship is given by:
where
is the torque, measured in newton-metres, is the magnetic moment, measured in ampere-square metres, and 
is the magnetic field, measured in newtons per (ampere-metre).
The alignment of the magnetic moment with the field creates a difference in potential energy U:
[edit] Magnetic moment of electrons
Electrons and many nuclei also have intrinsic magnetic moments, an explanation of which requires a quantum mechanical treatment and relates to the intrinsic angular momentum of the particles as discussed in the article electron magnetic dipole moment. It is these intrinsic magnetic moments that give rise to the macroscopic effects of magnetism, and other phenomena, such as nuclear magnetic resonance.
The magnetic moment of the electron is:
where 
= 2 in Dirac mechanics, but is slightly larger due to quantum electrodynamics effects.
Again it is important to notice that is a negative constant multiplied by the spin, so the magnetic moment is antiparallel to the spin angular momentum. This can be understood with the following classical picture: if we imagine that the spin angular momentum is created by the electron mass spinning around some axis, the electric current that this rotation creates spins in the opposite direction, because of the negative charge of the electron; such current loops produce a magnetic moment which is antiparallel to the spin angular momentum..
[edit] Magnetic moments of nuclei
The nuclear system is a complex physical system consisting of nucleons, i.e., protons and neutrons. The quantum mechanical properties of the nucleons include the spin among others. Since the electromagnetic moments of the nucleus depends on the spin of the individual nucleons, one can look at these properties with measurements of nuclear moments, and more specifically the nuclear magnetic dipole moment.
The nuclear magnetic moment is very sensitive to the individual contributions from nucleons and a measurement or prediction of its value can reveal important information about the content of the nuclear wavefunction. There are several theoretical models that predict the value of the magnetic dipole moment and a number of experimental techniques aiming to carry out measurements in nuclei along the nuclear chart.
