Displacement Current — Question 5

Question 5

A dielectric separates vacuum displacement from polarization current

A linear nonmagnetic dielectric of relative permittivity kappa completely fills a fixed parallel-plate capacitor. Use $D=\kappa\epsilon_0E$ and $P=(\kappa-1)\epsilon_0E$. Free charging current is I.

1. Find the vacuum displacement contribution and polarization-current contribution across the plate area.

2. Evaluate their fractions for kappa=5 and verify the total generalized current.

Question 5 - Solution

A dielectric separates vacuum displacement from polarization current

(a) Method and calculation

$$I=A\dot D=\kappa\epsilon_0A\dot E.$$$$\boxed{I_{d,0}=\epsilon_0A\dot E=I/\kappa}.$$

(b) Interpretation and further calculation

$$I_P=A\dot P=(\kappa-1)\epsilon_0A\dot E.$$$$\boxed{\kappa=5:\ I_{d,0}=I/5,\ I_P=4I/5,\ I_{d,0}+I_P=I}.$$

Physical check

Using only the vacuum term inside a dielectric omits the current associated with changing polarization.