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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.
A proton is a stable subatomic particle, symbol p, H +, or 1 H + with a positive electric charge of +1 e (elementary charge).Its mass is slightly less than the mass of a neutron and approximately 1836 times the mass of an electron (the proton-to-electron mass ratio).
The proton mass m p is composed primarily of gluons, and of the quarks (the up quark and down quark) making up the proton. Hence m p, and therefore the ratio μ, are easily measurable consequences of the strong force. In fact, in the chiral limit, m p is proportional to the QCD energy scale, Λ QCD.
Spin and magnetic moment are in the same direction for γ > 0 (as for protons). Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency.
where m n is the mass of the neutron, m p is the mass of the proton, m ν is the mass of the electron antineutrino, and m e is the mass of the electron; and the K are the corresponding kinetic energies. The neutron has no initial kinetic energy since it is at rest. In beta decay, a typical Q is around 1 MeV.
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).
This gives Q = 0.666 661 (7). [a] No matter what masses are chosen to stand in place of the electron, muon, and tau, the ratio Q is constrained to 1 / 3 ≤ Q < 1. The upper bound follows from the fact that the square roots are necessarily positive, and the lower bound follows from the Cauchy–Bunyakovsky–Schwarz inequality.
The elementary charge, usually denoted by e, is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 e) or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 e.