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The electric susceptibility χ_{e} of a dielectric material is a measure of how easily it polarizes in response to an electric field. This, in turn, determines the electric permittivity of the material and thus influences many other phenomena in that medium, from the capacitance of capacitors to the speed of light.## Dispersion and causality

## See also

It is defined as the constant of proportionality (which may be a tensor) relating an electric field E to the induced dielectric polarization density P such that

- $$

where $,\; varepsilon\_0$ is the electric permittivity of free space.

The susceptibility of a medium is related to its relative permittivity $,\; varepsilon\_r$ by

- $chi\_e\; =\; varepsilon\_r\; -\; 1.$

So in the case of a vacuum,

- $chi\_e\; =\; 0.$

The electric displacement D is related to the polarization density P by

- $$

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

- $mathbf\{P\}(t)=varepsilon\_0\; int\_\{-infty\}^t\; chi\_e(t-t\text{'})\; mathbf\{E\}(t\text{'}),\; dt\text{'}.$

That is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by $chi\_e(Delta\; t)$. The upper limit of this integral can be extended to infinity as well if one defines $chi\_e(Delta\; t)\; =\; 0$ for $Delta\; t\; <\; 0$. An instantaneous response corresponds to Dirac delta function susceptibility $chi\_e(Delta\; t)\; =\; chi\_e\; delta(Delta\; t)$.

It is more convenient in a linear system to take the Fourier transform and write this relationship as a function of frequency. Due to the convolution theorem, the integral becomes a simple product,

- $mathbf\{P\}(omega)=varepsilon\_0\; chi\_e(omega)\; mathbf\{E\}(omega).$

This frequency dependence of the susceptibility leads to frequency dependence of the permittivity. The shape of the susceptibility with respect to frequency characterizes the dispersion properties of the material.

Moreover, the fact that the polarization can only depend on the electric field at previous times (i.e. $chi\_e(Delta\; t)\; =\; 0$ for $Delta\; t\; <\; 0$), a consequence of causality, imposes Kramers–Kronig constraints on the susceptibility $chi\_e(0)$.

- Application of tensor theory in physics
- Magnetic susceptibility
- Maxwell's equations
- Permittivity
- Clausius-Mossotti relation

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Last updated on Thursday August 07, 2008 at 02:25:19 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Thursday August 07, 2008 at 02:25:19 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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