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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.
Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge. Thus, an object's charge can be exactly 0 e, or exactly 1 e, −1 e, 2 e, etc., but not 1 / 2 e, or −3.8 e, etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The magnitude of the electrical charge of one mole of elementary charges (approximately 6.022 × 10 23, the Avogadro number) is known as a faraday unit of charge (closely related to the Faraday constant). One faraday equals 9.648 533 212... × 10 4 coulombs. [5]
Electrons have an electric charge of −1.602 176 634 × 10 −19 coulombs, [80] which is used as a standard unit of charge for subatomic particles, and is also called the elementary charge. Within the limits of experimental accuracy, the electron charge is identical to the charge of a proton, but with the opposite sign. [83]
Related to the Faraday constant is the "faraday", a unit of electrical charge. Its use is much less common than of the coulomb, but is sometimes used in electrochemistry. [4] One faraday of charge is the charge of one mole of elementary charges (or of negative one mole of electrons), that is, 1 faraday = F × 1 mol = 9.648 533 212 331 001 84 × ...
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The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere). The charges must not overlap (e.g. they must be distinct point charges). The charges must be stationary with respect to a nonaccelerating frame of reference. The last of these is known as the electrostatic approximation. When movement ...