Electric Potential across a Boundary

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Discussion Overview

The discussion revolves around the concept of electric potential across a boundary in a uniform electric field, specifically addressing the conditions under which the electric potentials inside and outside an object must be equal at the boundary. Participants explore the implications of this equality and the factors that may influence it, including the presence of charges and the material properties of the boundary.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant states that the electric potential inside an object (\Phi_{in}) and outside (\Phi_{out}) must be equal at the boundary to avoid divergence of the electric field.
  • Another participant questions the necessity of this equality, suggesting that it may depend on factors such as the presence of charge on the boundary and the material properties (metal vs. plastic) of the boundary.
  • A later reply clarifies that in an electrostatic case, electrons would not be moving, and there would be no free charges on the boundary, although the role of boundary material remains uncertain.
  • One participant explains that if the potential changes abruptly at the boundary, the electric field would become infinitely strong, leading to divergence.
  • Another participant adds that divergence could be acceptable and notes that surface charges can arise even with insulators (dielectrics).

Areas of Agreement / Disagreement

Participants express differing views on whether the equality of electric potentials at the boundary is universally applicable, with some suggesting it may depend on specific conditions related to charge and material properties. The discussion remains unresolved regarding the conditions under which the potentials must be equal.

Contextual Notes

Participants mention various assumptions, including the electrostatic case and the absence of free charges, but these assumptions are not universally accepted or clarified, leading to potential limitations in the discussion.

Apteronotus
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Hi everyone,

I have a uniform electric field in which I place an object. I have read that the electric potential inside my object, [tex]\Phi_{in}[/tex], and the one on the outside, [tex]\Phi_{out}[/tex] must be equal at the boundary.
(ie. [tex]\Phi_{in}[/tex]=[tex]\Phi_{out}[/tex] on the boundary)
I don't understand why this is so. Can anyone shed some light.

Thanks in advance.
 
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Otherwise the electric field(=gradiant of the potential) at the boundary will diverge.
 
I really have no background in physics or electricity. Could you explain further?
1. what do you mean diverge?
2. why would it diverge?
 
1. I mean that the magnitude of the electric field is infinite.
2. [itex]-\frac{\partial \Phi}{\partial x_i}=E_i[/itex].
This implies that if the potential changes abruptly the electric field will be infinitely strong.
 
Apteronotus said:
Hi everyone,

I have a uniform electric field in which I place an object. I have read that the electric potential inside my object, [tex]\Phi_{in}[/tex], and the one on the outside, [tex]\Phi_{out}[/tex] must be equal at the boundary.
(ie. [tex]\Phi_{in}[/tex]=[tex]\Phi_{out}[/tex] on the boundary)
I don't understand why this is so. Can anyone shed some light.

Thanks in advance.

Hmmm, is that true? Seems it should depend on whether there is charge on the boundary, whether the boundary is made of metal or of plastic etc. And also whether the electrons are moving, or have reached their final positions.
 
I'm assuming an electrostatic case, so I guess the electrons would not be moving. Second, there are no free charges on the boundary.
I'm not really sure how the boundary material would come into play.
 
weejee said:
Otherwise the electric field(=gradiant of the potential) at the boundary will diverge.


the electric field would be infinite if the potential jumped at the boundary. divergence would be acceptable. one will get surface charges even with an insulator (dielectric).
 

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