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Boundary conditions at interfaces
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Fields change in defined ways across surfaces.
Across a charged surface the normal component of E jumps by σ/ε₀, while the tangential component is continuous. These conditions fix the fields in problems with dielectrics and conductors.
Surface of a conductor: E_tangential = 0.
D (not E) normal component has jump σ_free.
In more detail
At the boundary between two media, the component of the electric field parallel to the boundary is continuous, while the perpendicular component may jump by the surface charge divided by ε0.
Real-world uses
- Engineers analyse fields at insulator-conductor interfaces.
- Designing capacitors with multiple dielectric layers.
- Physicists use boundary conditions to match the fields on either side of a charged surface or a dielectric interface.
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Frequently asked questions
Is the tangential field continuous?
Yes, for static fields, the tangential component does not change across a boundary.
When does the normal field jump?
When there is surface charge at the boundary.
What is continuous across a charged surface?
The tangential electric field is continuous, while the normal component jumps by the surface charge over epsilon zero.
Related topics in Electrostatics
Method of images · Poisson's and Laplace's equations · Multipole expansion · Electrostatic energy of a sphere · Earnshaw's theorem · Electric field of a ring