Electric Field Distribution of a Charged Disk: The Role of Symmetry

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Discussion Overview

The discussion centers on the electric field distribution of charged disks and surfaces, particularly focusing on the role of symmetry in determining the direction of electric field lines. Participants explore theoretical implications and reasoning related to electric fields in various geometries, including infinite disks and large flat surfaces.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions why electric field lines would be perpendicular to an infinitely wide and long disk with a constant charge density.
  • Another participant argues that due to the rotational symmetry of the infinite disk, if the electric field were not perpendicular, it would lead to a contradiction, thus necessitating that the electric field must point along the perpendicular.
  • A participant inquires about the electric field distribution if the charged object is a large flat surface rather than a disk, suggesting that the field at the center should be approximately constant.
  • In response, another participant clarifies that an infinite sheet also exhibits rotational symmetry, and thus the same reasoning about the electric field direction applies.

Areas of Agreement / Disagreement

Participants generally agree on the implications of symmetry for the electric field direction in the context of infinite disks and sheets, but the discussion remains exploratory without a definitive conclusion on all aspects raised.

Contextual Notes

The discussion does not address specific mathematical formulations or assumptions that may influence the conclusions drawn about electric field behavior in different geometries.

Nikitin
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Hey. Let's say you have an infinitely wide and long disk with a thickness h. Inside the disk, there is a constant charge density ρ0.

Why would the electric field lines be perpendicular to the disk?

Can somebody explain how symmetry and such generally affect electric field distribution of a charged object?

thanks! :)
 
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Hi Nikitin. Assume that at some point on the disk, the electric field vector points at an angle away from the perpendicular. Note that the system (infinite disk) exhibits rotational symmetry about this point so if I rotate by ##\pi## radians, the electric field must remain unchanged. However, this rotation will take the electric field vector and make it point in the opposite direction but the rotation must leave the electric field at this point unchanged so it must simultaneously point in the original direction as well, which is a contradiction. Thus, the electric field vector must point along the perpendicular in order to avoid this contradiction.
 
hmm, that's a very smart trick! thanks allot!

But what if the object is not a disk, but a random, very large "flat" surface with a thickness h and constant charge density?

If the surface is large enough, shouldn't the field at its centre be approximately constant? Why?
 
Do you mean like an infinite sheet? An infinite sheet has no absolute center i.e. if you pick any point on the sheet, the sheet will look rotationally symmetric about that point. Consequently, the same argument from before applies.
 
Okay, thanks!
 
Good luck in your studies friend!
 

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