Question

At the planar interface of two dielectrics, which of the following statements related to the electric field (\(\vec{𝐸}\) ), electric displacement (\(\vec{D}\)) and polarization (\(\vec{P}\) ) is true ?

• A. Normal component of both \(\vec{𝐷}\) and \(\vec{𝑃}\) are continuous
• B. Normal component of both \(\vec{𝐷}\) and \(\vec{E}\) are discontinuous
• C. Normal component of \(\vec{D}\) is continuous and that of \(\vec{𝑃}\) is discontinuous
• D. Normal component of both \(\vec{𝐸}\) and \(\vec{𝑃}\) are continuous

Answer 1

The Correct Option is B

To understand the behavior of the electric field (\(\vec{E}\)), electric displacement (\(\vec{D}\)), and polarization (\(\vec{P}\)) at the interface between two dielectric materials, let’s go through the concepts systematically:

1. At the interface of two dielectrics, the boundary conditions for the normal and tangential components of the electric field and displacement vectors must be considered:
   • The normal component of the electric displacement vector \(\vec{D}\) is discontinuous in the presence of a surface charge. The discontinuity is given by the equation: \(D_{1n} - D_{2n} = \sigma_f\), where \(\sigma_f\) is the free surface charge density.
   • The polarization \(\vec{P}\) relates to the bound charge, and changes in medium polarization may cause discontinuities in its normal component. 
   • While discussing \(\vec{E}\), we know that the tangential components of \(\vec{E}\) are continuous, but normal components may differ due to dielectric constants of the materials, making the normal component discontinuous across the boundary.
2. Given these equations and boundary conditions, we can reason about the options:
   • The claim that the normal component of both \(\vec{D}\) and \(\vec{E}\) are discontinuous can be supported by boundary conditions. Since both are subject to changes at the dielectric boundary, the statement is indeed true.
   • Other options can be ruled out because either they propose continuity where there is typically discontinuity or they incorrectly associate properties of different components.

Conclusion: Based on the above analysis, the correct choice is that the normal component of both \(\vec{D}\) and \(\vec{E}\) are discontinuous at the interface of two dielectrics.