Boundary conditions of electric field?

In summary, the conversation discusses the confusion around a concept in Griffiths Electrodynamics regarding the equation for the Electric field near a surface with a surface charge density. The confusion arises from the presence of a negative sign in front of the E field in the equation. The discussion suggests that the equation should be modified to 2E =(1/εo)σ instead of E_above — E_below =(1/εo) σ, unless there is an external electric field involved. The issue of the orientation of a picture is also mentioned.
  • #1
PhysicsKid0123
95
1
I'm reading griffiths electrodynamics and I am confused about a concept. Mainly because I might be interpreting it in different ways. Why does the equation contain an E with a negative in front? Namely, E_below. Isn't the Electric field pointing away from the surface with the surface charge density and isn't the surface differential also pointing away from the surface? So when using gaus's law, shouldn't the equation be EA +EA =(1/εo)σA or 2E =(1/εo)σ rather than E_above — E_below =(1/εo) σ. This doesn't make sense unless we are talking about an external electric field that is propagating towards and across the surface. Because in that case the dot product of the external electric field and surface differential, one will be positive and one will be negative. But if this is the case, what about the electric field from the surface charge itself? After all, guas's law is relating the electric field coming from the surface and the surface charge density. Can someone clarify what is happening?PS. I've included the pages. One of the pictures doesn't want to change orientation even after rotating it and uploading it again.
image.jpg
image.jpg
 
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  • #2
Think of it as ##\vec E_{above}\cdot (dA\hat z) + \vec E_{below}\cdot (dA(-\hat z))=
((\vec E_{above})_z - (\vec E_{below})_z)dA##
 
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Related to Boundary conditions of electric field?

1. What are boundary conditions of electric field?

Boundary conditions of electric field refer to the rules that govern how the electric field behaves at the interface between two different materials or regions. These conditions determine how the electric field is affected by the presence of a boundary, and are an important concept in understanding the behavior of electric fields in various scenarios.

2. How do boundary conditions affect the behavior of electric field?

Boundary conditions can have a significant impact on the behavior of electric fields. For example, they can determine whether the electric field is continuous or discontinuous at a boundary, or how the electric field is reflected or transmitted at an interface between two materials. In some cases, boundary conditions can also affect the strength or direction of the electric field at a boundary.

3. What are some common types of boundary conditions for electric field?

Some common types of boundary conditions for electric field include continuity conditions, which require that the electric field is continuous across a boundary, and interface conditions, which describe how the electric field is affected by the presence of an interface between two materials. Other types of boundary conditions include symmetry conditions, which are based on the symmetry of the system, and charge conservation conditions, which ensure that the total electric field at a boundary is equal to the total charge present.

4. How are boundary conditions of electric field determined?

Boundary conditions of electric field are determined through a combination of theoretical analysis and experimental data. Theoretical models and equations can help predict the behavior of electric fields at boundaries, while experimental measurements can be used to validate these predictions and refine the understanding of boundary conditions. In some cases, boundary conditions may also be determined by considering the properties of the materials or interfaces involved.

5. Why are boundary conditions important in the study of electric field?

Boundary conditions are important in the study of electric field because they help us understand how electric fields behave in different situations. By considering the behavior of electric fields at boundaries, we can gain insight into the properties and interactions of materials, as well as the fundamental principles that govern electric fields. Boundary conditions are also essential for predicting and designing the behavior of electric fields in various applications, such as electronics, electromagnetics, and plasma physics.

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