Electric susceptibility

The electric susceptibility χ_e is the proportionality constant linking the polarization density P of a linear dielectric to the electric field E inside it: P = ε₀ χ_e E. It is dimensionless, positive for ordinary insulators, and it captures everything about how easily a material's bound charges shift in response to a field. Vacuum has χ_e = 0 (no charges to polarize). Air is barely polarizable (χ_e ≈ 5 × 10⁻⁴). Common solid insulators range from 1 to 10. Liquid water, with its large permanent dipole moment, reaches χ_e ≈ 79.

Susceptibility is a pure material property — it does not depend on geometry, only on what the material is made of and what conditions (temperature, frequency, applied DC field) it is sitting in. For most everyday dielectrics in modest fields, χ_e is a single positive number. For anisotropic crystals, it becomes a tensor whose principal axes pick out the natural directions of the crystal lattice. For nonlinear materials at high field strengths, χ_e itself depends on E, and the resulting nonlinear susceptibilities are the foundation of every laser-frequency-doubling crystal.

Susceptibility is the natural microscopic variable; permittivity ε = ε₀(1 + χ_e) is the macroscopic one that shows up in field equations. The two are linked by definition. Calculating χ_e from first principles requires quantum mechanics (the polarisability of each atom or molecule, summed over the density of atoms), but measuring it is straightforward — fill a parallel-plate capacitor with the material, see how much extra charge it holds at fixed voltage, divide by the vacuum value.