# What is the true meaning of the fields $\mathbf D (\mathbf r, t)$ and $\mathbf H (\mathbf r, t)$?

The meaning of the electric field is

$$\mathbf E = \frac{\text{force}}{\text{unit charge}}$$ the meaning of the polarization field is $$\mathbf P = \frac{\text{electric dipole moments}}{\text{unit volume}}$$ For the magnetic field is $$\mathbf B = \frac{\text{force}}{\text{unit charge moving with unit velocity such that the force is maximum}}$$ The magnetization field is the $$\mathbf M = \frac{\text{magnetic dipole moments}}{\text{unit volume}}$$

Question:

I know the definitions of the fields $$\mathbf D$$ and $$\mathbf H$$ as $$\mathbf D = \varepsilon_0 \mathbf E + \mathbf P \\ \mathbf H = \frac{1}{\mu_0} \mathbf B - \mathbf M$$

Is there such a simple meaning for the fields $$\mathbf D$$ and $$\mathbf H$$ similar to those of $$\mathbf E, \mathbf P, \mathbf B$$ and $$\mathbf M$$ ?

Think flux-density (from Gauss's law): $$\mathbf D = \frac{\text{free charge on one capacitor plate}}{\text{area of capacitor plate}}$$
Think circulation-density (from Ampere's Law): $$\mathbf H = \frac{\text{free current in coil}}{\text{length of coil}}$$
• ${\bf H}$ is the force on a unit magnetic monopole --- if you can find one.... Mar 21 at 23:41