Fields at the ends of a parallel plates

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Discussion Overview

The discussion revolves around the behavior of electric field lines at the ends of finite-length parallel plates, particularly why the field lines bulge outward rather than inward. The scope includes conceptual understanding and theoretical explanations related to electrostatics.

Discussion Character

  • Conceptual clarification, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions why the field lines bulge outward at the ends of finite-length plates, contrasting this with the uniform field between infinitely long plates.
  • Another participant suggests that the field lines prefer to go perpendicular to the surface, indicating that this results in an outward bulging at the ends.
  • It is proposed that the behavior of the field lines can be likened to a dipole configuration, which may help explain the outward bulging.
  • A different explanation is offered, stating that the configuration must minimize total energy, with inward curving of lines leading to increased field strength and higher stored energy, thus favoring an outward spread of the lines.

Areas of Agreement / Disagreement

Participants present multiple explanations for the bulging of field lines, indicating that there is no consensus on a single definitive reason. The discussion remains unresolved with competing views on the underlying principles.

Contextual Notes

The discussion does not clarify the assumptions behind the explanations provided, such as the specific conditions under which the energy minimization argument holds or the implications of the dipole analogy.

Pranav Jha
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Why do the field lines bulge out at the ends of plates with finite lengths? I understand why the field is uniform between infinitely long plates but cannot extend the concept to plates with fixed length:(

I know they have to bulge but why not bulge inwards rather than outwards?
 
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Hi Pranav Jha! :smile:

Basically, it's because they prefer to go perpendicular to the surface …

at the end, that's outward! :wink:
 
Another explanation comes from realizing that the configuration must have minimal total energy. Curving the lines inwards increases the field strength in between the plates, leading to higher stored energy. (Energy is proportional to the square of the density of flux lines.) Energy is minimized when the lines spread out into space with low density.
 

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