Why does an electron have a magnetic moment?

The magnetic moment of magnets is a measure that describes the magnetic force that a magnet exerts on electric currents as well as the torque that a magnetic magnetic field exerts on it. Magnetic moments can be found in a loop of electric currents, a bar magnet and an electron. The magnetic moment and magnetic fields can both be considered vectors with a magnitude or direction. The magnetic moment’s direction is from the magnet’s south pole to its north pole. Magnetic moment is also a factor in the magnetic field that a magnet produces. The term magnetic moment is used to refer to the system’s magnetic dipole moments, which produce the first term of the multipole expansion. The dipole component in an object’s magnet field is symmetric around the direction of its electromagnetic dipole moment and decreases with increasing distance.

Magnetic moment of an Atom
To get an atom’s total spin, each electron spin is added. Individual orbital angular moments are then added to create a total orbital momentum. To get the total angular momentum, these two are combined using angular momentum coupling. The magnitude of an atomic dipole moment can then be calculated.

where J is the total magnetic momentum quantum number, and gJ the Lande g factor. mB is Bohr’s magneton. This magnetic moment is the component that runs in the direction of magnetic field.
where m can be either the magnetic or the equatorial quant number. It can also take any 2J+1 value.
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Because electrons are charged with negative charges, the negative sign is created.
Because of the angular momentum, the dynamics for a magnetic dipole within a magnetic field is different from an electric dipole within an electric field. However, the magnetic field exerts a torque on the magnet dipole which tends to align it with its field. Precession is when the direction of spin changes. However, torque is proportional with the rate of change in angular momentum. This behavior is described by the Landau-Lifshitz-Gilbert equation

Magnetic fields are created by currents in wires. The magnetic field produced by a bar magnet where there are no wires is what? Is that why the field looks like a solenoid field?

The Bohr model shows electrons traveling in circular orbits around the nucleus. A circular orbit of an electron looks like a current loop with a current.

I = e/T = Ev/2pr

A current loop has an magnetic moment of m. For the orbiting electron, we get:

m = IA = (ev/2pr) * (pr2) = evr/2

Multiplying top and bottom with m, the electron mass will give us mvr. This is L, the orbital angle momentum of an electron.

According to the Bohr model, therefore, m = EL/2m. The orbital magnetic moment is proportional to the electron’s orbital angular momentum. Multiples of h_bar= h/2p are used to quantify the orbital angular momentum, where h is Planck’s constant. Bohr’s model is quite simplistic. Quantum mechanics analysis shows that the electron’s orbital magnet moment has a small non-zero value.

m = (2)1/2 e h_bar /2m

An electron spin is another contributor to the atom’s magnet moment. The electron spin magnetic moment is:

mspin = e h_bar/2m

This combination is called the Bohr magneton.

mB = e h_bar/2m = 9.27 x 10-27 J/T

The vector sum of the atom’s orbital and spin magnet moments is called the net magnetic moment. Many materials don’t have magnetic properties, i.e. they don’t behave like bar magnets. This is because their magnetic moments cancel or are completely cancelled. You can make bar magnets from materials, but neighboring atoms must interact so that their magnetic moments align. The material creates a magnetic field by acting as a current loop.

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