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In atomic physics, the effective nuclear charge of an electron in a multi-electron atom or ion is the number of elementary charges an electron experiences by the nucleus. It is denoted by Z eff . The term "effective" is used because the shielding effect of negatively charged electrons prevent higher energy electrons from experiencing the full ...
The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by [1] =, where μ is the spin magnetic moment of the particle, g is the g-factor of the particle, e is the elementary charge, m is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ħ/2 for Dirac particles).
where is the angular frequency, [1] is the magnitude of the applied magnetic field, and is the gyromagnetic ratio for a particle of charge, [2] equal to , where is the mass of the precessing system, while is the g-factor of the system.
When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
The invariant mass of an electron is approximately 9.109 × 10 −31 kg, [80] or 5.489 × 10 −4 Da. Due to mass–energy equivalence, this corresponds to a rest energy of 0.511 MeV (8.19 × 10 −14 J). The ratio between the mass of a proton and that of an electron is about 1836.
In his theory, the longitudinal mass = and the transverse mass =, where is the Lorentz factor and is the rest mass of the electron. [5] The concept of (transverse) electromagnetic mass m T {\displaystyle m_{T}} , which was based on specific models of the electron, was later transmuted into the purely kinematical concept of relativistic mass ...
The spin angular momentum of an electron is 1 / 2 ħ, but the intrinsic electron magnetic moment caused by its spin is also approximately one Bohr magneton, which results in the electron spin g-factor, a factor relating spin angular momentum to corresponding magnetic moment of a particle, having a value of approximately 2. [15]
Also, gravitational forces are much weaker than electrostatic forces. [2] Coulomb's law can be used to derive Gauss's law, and vice versa. In the case of a single point charge at rest, the two laws are equivalent, expressing the same physical law in different ways. [6]