Dielectrics

A dielectric is an insulator that can be polarized when external Electric Field is applied.

Polarization Vector

Calculating the induced charge, we use

For Surface Charge (${\rho }_s$) ${\rho }_s=\vec{P}\cdot \hat{n}$

For Volume Charge (${\rho }_v$) ${\rho }_v=-\nabla \cdot \vec{P}$

We use the Electric Flux Displacement Vector $\vec{D}$ to describe how much the electric field is affected by $\vec{P}$.

Boundary Conditions for Dielectrics

For the tangential boundary condition: $E_{1t}=E_{2t}$ For the normal boundary condition: $D_{1n}=D_{2n}$

Dielectric inside Capacitor

When a capacitor is charged to certain voltage, then disconnected from the battery, the charge of the plates is $Q_0=C_0\Delta V_c$

When we insert the dielectric between the plates of the capacitor, the capacitance will increase. Let’s see why. The charge on the capacitor doesn’t change, since the dielectric (insulator) desn’t allow charge to move through it. $Q=Q_0$

When we insert the dielectric between the parallel pates, atoms become locally polarized. This creates an electric field opposite to the electric field from the plates of the capacitor. The net electric field is now weakened. Since potential depends on the electric field, it is also weakened. From the formula, $Q=CV$, since Q remains constant and V decreases, C must necessarily increase.

Related

• Capacitor