How insulators respond to electric fields — and why they multiply capacitance.
A dielectric is an insulating material that, when placed in an electric field, develops electric dipoles throughout its volume. It does not allow charge to flow (unlike a conductor), but it responds to the field by internally reorganising its charge distribution.
In the absence of a field, the positive and negative charge centres in each molecule coincide — no net dipole. When a field is applied, these charges shift slightly: positive charges shift in the direction of \( \vec{E} \), negative charges against it. Each molecule becomes an electric dipole. This process is called polarisation.
Molecules with no permanent dipole moment (e.g., \( \text{O}_2 \), \( \text{H}_2 \), \( \text{CO}_2 \)). Dipoles are induced only when a field is applied. The induced dipole moment is proportional to the applied field.
Molecules with a permanent dipole moment (e.g., \( \text{H}_2\text{O} \), \( \text{HCl} \)). In the absence of a field, the dipoles are randomly oriented due to thermal motion, giving zero net polarisation. An external field partially aligns them — both rotating the existing dipoles and inducing a small additional moment.
The polarisation \( \vec{P} \) is defined as the electric dipole moment per unit volume:
\[ \vec{P} = \frac{\text{net dipole moment}}{\text{volume}} \quad \text{(unit: C/m}^2\text{)} \]For a linear dielectric, \( \vec{P} \) is proportional to the applied electric field:
\[ \vec{P} = \varepsilon_0 \chi_e \vec{E} \]where \( \chi_e \) is the electric susceptibility of the dielectric. The dielectric constant (relative permittivity) is related by \( K = \varepsilon_r = 1 + \chi_e \).
The aligned dipoles produce a layer of positive bound charge on one surface of the dielectric slab and negative bound charge on the opposite surface. These bound surface charges set up a field \( \vec{E}_p \) inside the dielectric that opposes the applied field:
\[ E_{\text{inside}} = E_0 - E_p = \frac{E_0}{K} \]The surface charge density of the bound charges is:
\[ \sigma_b = P = \varepsilon_0 \chi_e E_{\text{inside}} \]