Question

State the SI unit of the electric potential polarization vector $P$.

Answer 1

Hint: Electric polarization vector is a measure of the total permanent or induced dipole moment in a dielectric per its unit volume when kept in the presence of an external magnetic field. It is also called as polarization density and its SI unit can be found out by using the SI units of the physical quantities in its definition ratio, that is, electric dipole moment to volume.

Formula used:
$P=\dfrac{\Delta p}{\Delta V}$
where $P$ is the polarization density, $p$ is the electric dipole moment and $V$ is the volume of the element.

Complete step by step answer:
When a dielectric is placed in the presence of an external electric field, the electric dipoles get oriented in a certain fashion. Therefore, due to this induced dipole moment and the permanent dipole moment (present regardless of the external field), there is a net dipole moment induced in the dielectric. The electric polarization vector or polarization density is the magnitude of this net dipole moment per unit volume of the element.
Hence,
$P=\dfrac{\Delta p}{\Delta V}$ --(1)
where $P$ is the polarization density, $p$ is the electric dipole moment and $V$ is the volume of the element.
Now, the SI unit of electric dipole moment is Coulomb-meter $\left( C.m \right)$ and the SI unit of volume is meter cubed $\left( {{m}^{3}} \right)$. Hence, according to the definition in (1), the SI unit of electric polarization will be nothing but,
$\dfrac{C.m}{{{m}^{3}}}=\dfrac{C}{{{m}^{2}}}=C/{{m}^{2}}$
Hence, the SI unit of electric polarization is Coulomb per meter squared $\left( C/{{m}^{2}} \right)$.

Note: It is imperative that students know the definitions of some not so common electric and magnetic physical quantities like magnetization, electric polarization, electric moment and magnetic moment. These topics are usually not studied in much detail by students since they are small topics, however they hold prime importance in solving these and many such types of questions. Without the knowledge of these definitions, it is impossible to even attempt such questions. Therefore, students should not neglect these topics.