Boundary condition of EM field

In summary, the tangential components of electric fields on the boundary of two regions are continuous. It is unclear if this also applies to the tangential components of displacement or polarization. The boundary conditions for magnetic field are given by the equation (\vec{B}_{above} - \vec{B}_{below} )\cdot\hat{n} = 0 and (\vec{B}_{above} - \vec{B}_{below} )\times \hat{n} = \mu_0\vec{K}. There is uncertainty about what \vec{K} represents and if it is the same as free current surface density. The formula that relates D and E may provide insight into whether or not the tangential components of displacement or
  • #1
KFC
488
4
On the boundary (surface) of two regions, the tangential components of electric fields on above and below surface are continuous. I wonder if it is also true for displacement [tex]\vec{D}[/tex] and polarization [tex]\vec{P}[/tex]? That is, can I say:
the tangential component of [tex]\vec{D}[/tex] or [tex]\vec{P}[/tex] on above and below surface are continuous?

For magnetic field, the statement of the magnetic field about [tex]\vec{B}[/tex] is:

[tex](\vec{B}_{above} - \vec{B}_{below} )\cdot\hat{n} = 0[/tex]
and
[tex](\vec{B}_{above} - \vec{B}_{below} )\times \hat{n} = \mu_0\vec{K}[/tex]

I wonder if [tex]\vec{K}[/tex] means the free current surface density? What is the boundary conditions for [tex]\vec{H}[/tex]?
 
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  • #2
Do the two regions have the same dielectric constant? Think about the formula that relates D and E...
 
  • #3
Xezlec said:
Do the two regions have the same dielectric constant? Think about the formula that relates D and E...

That is the question. In the text, it said the tangential components of the electric fields on the boundary are continuous. But it doesn't tell if the tangential components of the displacement or polarization are also continuous or not. So if the dielectric constants in these two regions not the same, does it mean they will not be continuous even along the tangential direction?

By the way, in some text, it reads

[tex](\vec{P}_2-\vec{P}_1)\cdot\hat{n} = -\sigma_p[/tex]

and [tex]\sigma_p[/tex] is what we call the density of polarized charges. I wonder if this is the same name as bound charges which is used in other text?
 
Last edited:
  • #4
KFC said:
That is the question. In the text, it said the tangential components of the electric fields on the boundary are continuous. But it doesn't tell if the tangential components of the displacement or polarization are also continuous or not. So if the dielectric constants in these two regions not the same, does it mean they will not be continuous even along the tangential direction?

I was just saying that by looking at the formula that relates D and E, you will see the answer to that question. The dielectric constant is the constant of proportionality between D and E, so if E is continuous, but the dielectric constant changes, what is going to happen to D? See what I mean?
 

1. What are boundary conditions of an electromagnetic field?

The boundary conditions of an electromagnetic (EM) field refer to the rules that govern the behavior of the EM field at the interface between two different materials or regions. These conditions describe how the electric and magnetic fields behave at the boundary and are important for understanding the propagation of EM waves.

2. What is the importance of boundary conditions in EM field?

Boundary conditions are important because they help us understand how EM waves interact with different materials and how they can be controlled or manipulated. They also allow us to make predictions about the behavior of EM fields at interfaces, which is useful in many practical applications such as antennas and optical devices.

3. What are the two types of boundary conditions in EM field?

The two types of boundary conditions in EM field are the electric boundary condition and the magnetic boundary condition. The electric boundary condition describes the relationship between the electric field and the surface charge density at the boundary, while the magnetic boundary condition relates the magnetic field to the surface current density.

4. How are boundary conditions derived in EM field?

Boundary conditions are derived from Maxwell's equations, which are a set of equations that describe the behavior of electric and magnetic fields. These equations take into account the fundamental properties of EM waves, such as the conservation of charge and energy, and are used to determine the behavior of the fields at boundaries between different materials.

5. Can boundary conditions change depending on the materials involved?

Yes, boundary conditions can change depending on the materials involved. Different materials have different electrical and magnetic properties, which can affect the behavior of the EM field at the boundary. Therefore, the specific boundary conditions for a given interface will depend on the materials on either side of the interface.

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