Question

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

of P, one of E, and one of D. Assume L is about 2a. [Hint: E lines terminate on

charges; D lines terminate on free charges.]

Short answer

The required sketches are shown in Figures 1-3.

Step-by-step solution

Define the concept 

Consider the polarization vector as one thatpoints in the upward direction and has a magnitude and direction that is constant in nature:

Note the surface charges at the top or bottom is

${\mathbf{\sigma }}_b\mathbf{=}\mathbf{\pm }\mathbf{P}$

The above expression shows that the electric field terminates on the charges.

Consider the displacement field does not terminate on the charges, as the field lines either reach infinityor loop on themselves.

Determine the three sketches 

Consider the radius of the bar electret have the length of Lsuch that$(L=a)$.

Consider the diagram is shown in Figure 1

Consider for the polarization the field P is uniform as shown in Figure 2

The figure 2 shows the fieldsthat are identical with the field line pattern between the two circular plates.

Consider the diagram for the field line patterns for the electric displacement D that exists out of the bar and have the same pattern as of the electric field that is shown in Figure 2.

The required diagram is shown in Figure 3