For the bar electret of Prob. 4.11 , make three careful...

For the bar electret of Prob. 4.11 , make three careful sketches: one of $\mathbf{P}$, one of $\mathbf{E},$ and one of $\mathbf{D}.$ Assume $L$ is about $2 a$ .[Hint: $\mathbf{E}$ lines terminate on charges; $\mathbf{D}$ lines terminate on free charges.]

Key Concepts

Electret

An electret is a dielectric material that has a quasi-permanent electric polarization. Similar to a permanent magnet in magnetism, an electret maintains a static electric field because its internal molecular or structural alignment remains stable over time. This property is crucial in many applications such as sensors and transducers.

Polarization

Polarization, denoted by P, represents the dipole moment per unit volume within a material. It arises due to the alignment of microscopic electric dipoles in response to an external field or through intrinsic ordering. In the context of dielectric materials like electrets, polarization is responsible for the bound charges that contribute to the material’s overall electric behavior.

Electric Field

The electric field, designated by E, is a vector field that represents the force per unit charge at any point in space. It is produced by both free charges and the bound charges within materials. The field lines of E originate on positive charge and terminate on negative charge, and their configuration is influenced by both the intrinsic polarization of dielectrics and any externally applied charges.

Electric Displacement Field

The electric displacement field, indicated by D, is a vector field used primarily to account for the effects of free charges in the presence of dielectric materials. It is defined by the relationship D = ??E + P, combining both the electric field and the polarization. The field lines of D are particularly useful for identifying the locations of free charges since they terminate on them, simplifying the analysis of field distributions in materials.

Bound and Free Charges

In dielectric media, charges are categorized as either bound or free. Bound charges arise from the polarization of the material and are not free to move, while free charges are those that can move within or on the surface of the material. Understanding the distinction between these two is essential, as the electric field E is influenced by both types, whereas the displacement field D directly accounts for only free charges.

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