Why does charge build up at the boundary surface of two media?
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On a homework problem, we are asked to to use the first two Maxwell equations,
∇⋅B=0∇⋅B=0
∇⋅D=ρ∇⋅D=ρ
to show that along the boundary surface of two different media (different permittivity constants), the magnetic field component that is normal to that boundary is continuous, and also that the electric displacement field DD has a discontinuity on the surface because of the surface charge density on that boundary.
How do I show this? Am I supposed to show, through Maxwell's equations (the ones provided) that an electromagnetic four-potential causes surface charge density to accumulate on the boundary? Why does this happen?
∇⋅B=0∇⋅B=0
∇⋅D=ρ∇⋅D=ρ
to show that along the boundary surface of two different media (different permittivity constants), the magnetic field component that is normal to that boundary is continuous, and also that the electric displacement field DD has a discontinuity on the surface because of the surface charge density on that boundary.
How do I show this? Am I supposed to show, through Maxwell's equations (the ones provided) that an electromagnetic four-potential causes surface charge density to accumulate on the boundary? Why does this happen?
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Explanation:
Surface charge is a two-dimensional surface with non-zero electric charge.These electric charges are constrained on this 2-D surface, and surface charge density, measured.
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