Formula: Electric Susceptibility Using Microscopic Quantities Polarizability Volume Number of dipoles
$$ \class{green}{\chi_{\text e}} ~=~ \frac{ N \, \class{blue}{\alpha} }{ \varepsilon_0 \, V }$$
$$ \class{green}{\chi_{\text e}} ~=~ \frac{ N \, \class{blue}{\alpha} }{ \varepsilon_0 \, V }$$
$$\class{blue}{\alpha} ~=~ \frac{ \varepsilon_0 \, \class{green}{\chi_{\text e}} \, V }{ N }$$
$$V ~=~ \frac{ N \, \class{blue}{\alpha} }{ \varepsilon_0 \, \class{green}{\chi_{\text e}} }$$
$$N ~=~ \frac{ \varepsilon_0 \, \class{green}{\chi_{\text e}} \, V }{ \class{blue}{\alpha} }$$
Electric susceptibility
$$ \class{green}{\chi_{\text e}} $$ Unit $$ - $$
Electric susceptibility indicates how well a material can be polarized by an external electric field \( \class{purple}{E} \). In other words, it quantifies how effectively the external electric field is weakened or strengthened within the material.
- For \( \class{green}{\chi_{\text{e}}} > 0 \), the external electric field is amplified within the material.
- For \( \class{green}{\chi_{\text{e}}} < 0 \), the external electric field is weakened within the material.
- For \( \class{green}{\chi_{\text{e}}} = 0 \), it is neither weakened nor strengthened. The "material" is vacuum.
| Material | Electric susceptibility |
|---|---|
| Vacuum | 0 |
| Air (0°C) | 0.0005 |
| Glass | 4 bis 9 |
| Water (0°C) | 87 |
| Water (40°C) | 72.4 |
| Ice (-20°C) | 15 |
| Hydrogen Cyanide | 94 |
| Ethanol (20°C) | 24.8 |
Polarizability
$$ \class{blue}{\alpha} $$
Polarizability is a microscopic quantity that describes how effectively a molecule or atom can form a dipole. The unit of polarizability is \( \mathrm{Cm}^2 / \mathrm{V} \).
Volume
$$ V $$ Unit $$ \mathrm{m}^3 $$
The volume of a body exposed to an external electric field.
Number of dipoles
$$ N $$ Unit $$ - $$
Number of induced dipoles inside the polarized body.