CBSE Class 12-science Answered
Relation betwwen the POLARIZATION VECTOR and SURFACE CHARGE DENSITY of POLARIZATION CHARGES
Asked by pardeepkumar2281 | 18 May, 2018, 09:11: PM
Expert Answer
Let us consider a rectangular dielectric slab is placed in uniform external field.
The field causes a uniform polaraisation P of the dielectric.
Thus every volume element Δv of the slab has a dipole moment PΔv in the direction of the field.
The volume element Δv is macroscopically small but contains a very large number of moleculer dipoles.
Anywhere inside the dielectric, the volume element Δv has no net charge though it has dipole moment.
However at the surface of the dielectric normal to the electric field, there is a net charge density.
As seen in the figure, the positive ends of dipole remain unneutralised at the right surface and negative ends at the left surface.
The unbalanced charges are the induced charges due to external field.
Thus the polarised dielectric is equivalent to two charged surfaces with induced surface charge densities, say σP and -σP .
Clearly, the field produced by these surface charges opposes the external fiel.
The surface charge density ±σP arises from bound charge in the dielectric.
The relation between the induce charge density σP and the polarisation P is given by
where 
is unit vector along the outward normal to the surface as shown in figure.
is unit vector along the outward normal to the surface as shown in figure. As shown in figure, Polarisation vector is along the unit normal vector at right surface and opposite to unit normal at the left surface.
Hence induced charge density is positive at right surface. At left surface induced charge density is negative.
Answered by Thiyagarajan K | 21 May, 2018, 03:33: PM
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