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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 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:
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
The most important aspect of the EFIE is that it allows us to solve the radiation/scattering problem in an unbounded region, or one whose boundary is located at infinity. For closed surfaces, it is possible to use the Magnetic Field Integral Equation or the Combined Field Integral Equation, both of which result in a set of equations with ...
The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa 2 ·E, by Gauss's law equals πa 2 ·σ/ε 0. Thus, σ = ε 0 E. In problems involving conductors set at known potentials, the potential away from them is obtained by solving Laplace's equation, either analytically or ...
Quantity (common name/s) (Common) symbol/s SI units Dimension Number of wave cycles N: dimensionless dimensionless (Oscillatory) displacement Symbol of any quantity which varies periodically, such as h, x, y (mechanical waves), x, s, η (longitudinal waves) I, V, E, B, H, D (electromagnetism), u, U (luminal waves), ψ, Ψ, Φ (quantum mechanics).
If the body is at rest (v = 0), i.e. in its center-of-momentum frame (p = 0), we have E = E 0 and m = m 0; thus the energy–momentum relation and both forms of the mass–energy relation (mentioned above) all become the same. A more general form of relation holds for general relativity.
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.