Question

define and discuss electric field vectors D,E, and P. eastablise the following relations.
(i) D vector = epsilon E + P
(ii) del. D vector= Pf

Answer 1

Polarization vector, P = P is equal to the bound charge per unit area or equal to the surface density of bound charges (because surface charge density is charge per unit area),

Thus P = qb/A = σp (2)

Where qb is bound charge and σp is surface density of bound charges.

P is also defined as the electric dipole moment of material per unit volume.

P = np

where n is number of molecules per unit volume.

Displacement vector, D= D is equal to the free charge per unit area or equal to the surface density of free charges,

Thus D = q/A = σ (3)
where q is free charge and σ is surface density of free charges.

As for parallel plate capacitor (already derived in earlier articles):

E = σ /ε0 (4)

Ep = σp /ε0 (5)

By substituting equations 4 and 5 in equation 1, we get

E = σ /ε0 – σp /ε0

Or ε0E = σ – σ0

By putting equations 2 and 3 in above equation, we get

ε0E = D – P

or D = ε0E + P

This is the relation between D, E and P.
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