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The multipole expansion circumvents this difficulty by expanding not E or B, but r ⋅ E or r ⋅ B into spherical harmonics. These expansions still solve the original Helmholtz equations for E and B because for a divergence-free field F, ∇ 2 (r ⋅ F) = r ⋅ (∇ 2 F). The resulting expressions for a generic electromagnetic field are:
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.
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.) This is the reason for the terminology "elementary charge": it is meant to imply that it is an indivisible unit of charge.
The electrostatic CGS system implicitly sets 4πε 0 = 1, as commonly found in older physics literature, where the expression of the fine-structure constant becomes =. A nondimensionalised system commonly used in high energy physics sets ε 0 = c = ħ = 1 , where the expression for the fine-structure constant becomes [ 10 ] α = e 2 4 π ...
It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c 2, where c is the speed of light in vacuum (from E = mc 2). It is common to informally express mass in terms of eV as a unit of mass , effectively using a system of natural units with c set to 1. [ 3 ]
In physics, the coefficient of restitution (COR, also denoted by e), can be thought of as a measure of the elasticity of a collision between two bodies. It is a dimensionless parameter defined as the ratio of the relative velocity of separation after a two-body collision to the relative velocity of approach before collision.
The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions. Drude calculated the average drift velocity from p = −eEτ where p is the average momentum, −e is the charge of the electron and τ is the average time between the collisions. Since both the momentum and the ...
Since m 0 does not change from frame to frame, the energy–momentum relation is used in relativistic mechanics and particle physics calculations, as energy and momentum are given in a particle's rest frame (that is, E ′ and p ′ as an observer moving with the particle would conclude to be) and measured in the lab frame (i.e. E and p as ...