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Time value of money problems involve the net value of cash flows at different points in time. In a typical case, the variables might be: a balance (the real or nominal value of a debt or a financial asset in terms of monetary units), a periodic rate of interest, the number of periods, and a series of cash flows. (In the case of a debt, cas
Polarizability is responsible for a material's dielectric constant and, at high (optical) frequencies, its refractive index. The polarizability of an atom or molecule is defined as the ratio of its induced dipole moment to the local electric field; in a crystalline solid, one considers the dipole moment per unit cell. [1]
The time value of money means that money is worth more now than in the future because of its potential growth and earning power over time. In other words, receiving a dollar today is more valuable ...
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 nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The polarizability of individual particles in the medium can be related to the average susceptibility and polarization density by the Clausius–Mossotti relation. In general, the susceptibility is a function of the frequency ω of the applied field.
In general, a material cannot polarize instantaneously in response to an applied field, and so the more general formulation as a function of time is = (′) (′) ′. That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by χ e ( Δ t ) {\displaystyle \chi _{\text{e ...
The Lorentz–Lorenz equation is similar to the Clausius–Mossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its polarizability. The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz , who published it in 1869, and the Dutch ...
However, care is needed because some authors [6] take out the factor from (), so that = and hence () = /, which is convenient because then the (hyper-)polarizability may be accurately called the (nonlinear-)susceptibility per molecule, but at the same time inconvenient because of the inconsistency with the usual linear polarisability definition ...