Name: field behavior at dielectric interfaces
Uploaded: 2023-09-18T17:11:18.000Z
Duration: 1 min 27 s
Channel: JoVE

The electrostatic boundary condition gives the discontinuity of an electric field at a surface boundary. Consider the case where both the media across the boundary are dielectric materials.
Rewriting the electric field in terms of electric displacement shows that its tangential component is discontinuous across the interface.
For the normal component, consider a Gaussian pillbox on the interface. Rewriting Gauss&#39;s law in terms of electric displacement, the change in normal components at the interface gives the surface free charge density.
If no free charges exist at the boundary, the normal components are continuous across the interface. However, the electric field for the same is discontinuous.
Consider a perfect conductor in place of one of the dielectrics. The electric field inside a perfect conductor is zero. Substituting this in the dielectric-dielectric boundary conditions gives the boundary conditions at a conductor-dielectric interface.
If the other dielectric is removed, the material&#39;s permittivity equals the permittivity of free space. This gives the boundary conditions at a conductor-free space interface.

electrostatic boundary conditions in dielectrics

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity. Substituting the electric field in the electrostatic boundary conditions with the electric displacement shows that the tangential component of the electric displacement is discontinuous across the interface. But for the same case, the electric field is continuous. Similarly, the normal component of the electric field is discontinuous across the interface. However, the normal component of the electric displacement is continuous if there are no free charges at the boundary. 
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Consider replacing one of the dielectric materials with a perfect conductor. Applying the electric field inside a perfect conductor as zero gives the boundary conditions for a conductor-dielectric interface. If the other dielectric is removed, the material's permittivity equals free space's permittivity, as the dielectric constant's value for free space is 1. Substituting this in the conductor-dielectric boundary conditions gives the boundary conditions for a conductor-free space interface.

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the ...

electrostatic-boundary-conditions-in-dielectrics

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field behavior at dielectric interfaces

Field behavior at dielectric interfaces changes when an electric field crosses from one homogeneous medium into another. That change creates a discontinuity, or sudden jump, in the field. The boundary conditions depend on which materials meet at the interface.

When the two sides are different dielectric materials, the electric field and the electric displacement are linked through the material’s permittivity. Replacing the electric field with the electric displacement in the boundary conditions shows that the tangential component of the electric displacement is discontinuous across the interface. In the same situation, the electric field itself remains continuous.

The normal components change differently. The normal component of the electric field is discontinuous across the interface. The normal component of the electric displacement is continuous when no free charges are present at the boundary.

The boundary conditions also change when one dielectric is replaced by a perfect conductor. Inside a perfect conductor, the electric field is zero. Using that fact gives the boundary conditions for a conductor-dielectric interface.

If the dielectric is removed completely, the remaining medium is free space. Its permittivity is the same as free space permittivity, since the dielectric constant of free space is 1. Substituting this into the conductor-dielectric case gives the boundary conditions for a conductor-free space interface.

Field Behavior at Dielectric Interfaces

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Field behavior at dielectric interfaces changes when an electric field crosses from one homogeneous medium into another. That change creates a discontinuity, or sudden jump, in the field. The boundary conditions depend on which materials meet at the interface. When the two sides are different dielectric materials, the electric field and the electric displacement are linked through the material’s permittivity. Replacing the electric field with the electric displacement in the boundary...

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Learn how electric fields change at dielectric boundaries, including tangential and normal components, and how the rules shift for conductors and free space.

Field Behavior at Dielectric Interfaces | JoVE K12

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Field Behavior at Dielectric Interfaces

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