I'm in an upper division undergrad E&M course using Griffths' Electrodynamics text, and I've been struggling to understand the intuition/motivation behind the displacement field, D.

1)

In LIH dielectrics, P is proportional to E by the relationship

2)

Making the substitution with the original definition:

3)

To me, what these equations are saying is (please forgive my less than formal language, I'm making my best attempt)

1) The displacement field at some point within a dielectric (or anywhere, for that matter) is equal to the field within it, which is smaller in magnitude than the applied field, because it is weakened by the opposing field produced by the separation of charge at the outside edges of the dipole material (the "head" of one dipole canceling the oppositely charged "tail" of the neighboring dipole in the media) plus the Polarization (dipole moment per unit volume), which is in the opposite direction of the field generated by the dipole material which opposes the applied field (field due to free charge). By adding these two quantities, we essentially ignore the field of the dipole and retrieve something equal in magnitude to the field due to only the free charge.

This, to me makes sense, since the closed surface integral of D (dot) dA is equal to the free charge enclosed:

But what are 2) and 3) really saying?

If in 3) we say D = εE where E is the total field in the dielectric, multiplying by epsilon must serve to increase the magnitude of the RHS of the equation because D is also defined by the field of only the free charge, which must be greater than the field of the free charge minus the opposing field due to polarization.

but then how can 2) make sense? How can the polarization be larger in magnitude than the field in the dielectric?

I feel as though my understanding of something here must be completely backwards.

1)

**D**is defined as**(ε**, and is sometimes referred to as the flux density vector._{0}E + P)In LIH dielectrics, P is proportional to E by the relationship

2)

**P = ε**_{0}χ_{e}EMaking the substitution with the original definition:

3)

**D = (ε**(using the definition 1+χ_{0}E + ε_{0}χ_{e}E) → D = εE_{e}=ε_{r})To me, what these equations are saying is (please forgive my less than formal language, I'm making my best attempt)

1) The displacement field at some point within a dielectric (or anywhere, for that matter) is equal to the field within it, which is smaller in magnitude than the applied field, because it is weakened by the opposing field produced by the separation of charge at the outside edges of the dipole material (the "head" of one dipole canceling the oppositely charged "tail" of the neighboring dipole in the media) plus the Polarization (dipole moment per unit volume), which is in the opposite direction of the field generated by the dipole material which opposes the applied field (field due to free charge). By adding these two quantities, we essentially ignore the field of the dipole and retrieve something equal in magnitude to the field due to only the free charge.

This, to me makes sense, since the closed surface integral of D (dot) dA is equal to the free charge enclosed:

But what are 2) and 3) really saying?

If in 3) we say D = εE where E is the total field in the dielectric, multiplying by epsilon must serve to increase the magnitude of the RHS of the equation because D is also defined by the field of only the free charge, which must be greater than the field of the free charge minus the opposing field due to polarization.

but then how can 2) make sense? How can the polarization be larger in magnitude than the field in the dielectric?

I feel as though my understanding of something here must be completely backwards.

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