**The Resultant Electric Field of Permanent Dipoles in a Polar Dielectric is Zero due to Thermal Agitation**

**Explanation:**

Polar dielectrics are materials that possess permanent electric dipoles. These dipoles arise due to the presence of polar molecules or ions in the material. Each dipole consists of a positive charge and a negative charge separated by a small distance. In the absence of an external electric field, these dipoles are randomly oriented, resulting in a net zero electric field.

**Thermal Agitation:**
One of the main reasons for the resultant electric field of permanent dipoles in a polar dielectric being zero is thermal agitation. At finite temperatures, the molecules or ions in the polar dielectric undergo random thermal motion. This thermal agitation causes the dipoles to rotate and reorient themselves continuously.

**Random Orientation:**
As a result of thermal agitation, the dipoles in the polar dielectric undergo continuous rotational motion, leading to random orientations. The random nature of this motion ensures that, on average, there is an equal number of dipoles pointing in each direction. Thus, the net electric field generated by these dipoles cancels out, resulting in a zero resultant electric field.

**Symmetry:**
Another aspect that contributes to the zero resultant electric field is the symmetry of the material. Polar dielectrics often have a crystal lattice structure that possesses certain symmetries. These symmetries ensure that the dipoles are evenly distributed in all directions, further reinforcing the cancellation of the electric fields.

**External Electric Field:**
When an external electric field is applied to a polar dielectric, the dipoles tend to align themselves with the field. However, due to thermal agitation, the dipoles are not able to fully align and maintain their orientation. This leads to a partial alignment, resulting in a reduced net dipole moment and a weakened electric field within the dielectric.

**Conclusion:**
In summary, the resultant electric field of permanent dipoles in a polar dielectric is zero due to the combined effects of thermal agitation, random orientation, symmetry, and the inability of the dipoles to fully align in the presence of an external electric field. These factors ensure that the net dipole moment and electric field cancel out, resulting in a zero electric field within the material.

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