Question about a sheet of charge

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Discussion Overview

The discussion revolves around the electric field produced by different charge distributions, specifically focusing on point charges, line charges, sheet charges, and volume charges. Participants explore the implications of these models, particularly the behavior of electric fields at varying distances from the charge distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the validity of the claim that a sheet charge produces a constant electric field regardless of distance, suggesting that this leads to counterintuitive conclusions about the force experienced by distant objects.
  • Another participant emphasizes the assumption that the sheet of charge is infinite, noting that this is a common approximation that simplifies the analysis of the electric field close to the sheet.
  • There is a mention that for finite sheets, the electric field behaves differently at large distances, resembling that of a point charge, but obtaining a closed form solution for finite sheets is challenging.
  • Participants discuss the specific case of a finite disc and its electric field along the axis, indicating that it can yield a simple closed form solution, which approaches that of an infinite sheet as the radius increases.
  • One participant describes how a finite rectangular sheet can be analyzed by considering it as an infinite number of line charges, where only the perpendicular components contribute to the electric field.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the electric field produced by sheet charges, particularly regarding the assumptions of infinite versus finite sheets. There is no consensus on the validity of the claims made about the behavior of electric fields at large distances.

Contextual Notes

Limitations include the assumption of infinite charge distributions in deriving electric fields, which may not hold in practical scenarios. The discussion also highlights the complexity of deriving solutions for finite charge distributions.

toesockshoe
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Today my prof said that for a point charge the force is proportional to 1/r^2. For a line charge it is proportional to 1/r. For a sheet charge it is a constant and for a volume it is proportional to r. He also did some derivations but I don't see how this can be.

For example for a sheet charge how can a test charge that is a million meters away experience the same force that an object one millimeter away experiences? Then doesn't that mean if I make a sheet charge of say 100C, then I should be able to provide a resulting force on an object that is across the country ... because a sheet charge produces a uniform electric field regardless of position right? Obviously this doesn't happen because if someone create a sheet charge in Africa...a metal object here certainly doesn't not feel it all the way here in America. Same thing with a volume charge... How can an object further away from the charge feel a stronger attraction than something closer to the charge?
 
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It's always important to understand what assumptions are made when deriving these kinds of equations. In particular, the assumption when deriving the electric field of a sheet of charge is that the sheet is infinite in extent. Obviously, this is not physical, but it is a good approximation when looking at the electric field close to the sheet. It's like the acceleration due to gravity. Certainly objects don't always accelerate with an acceleration of ##g## (after all, the force decreases as you get farther from the Earth), but when close to the surface, it is a good approximation to treat the gravitational field as a constant.

If the sheet is finite, then at far distances, it will look like a point charge. Then you can imagine what the formula will look like, however, from searching around, it is very difficult to get a closed form solution for a finite sheet of charge, hence the infinite sheet approximation.
 
axmls said:
It's always important to understand what assumptions are made when deriving these kinds of equations. In particular, the assumption when deriving the electric field of a sheet of charge is that the sheet is infinite in extent. Obviously, this is not physical, but it is a good approximation when looking at the electric field close to the sheet. It's like the acceleration due to gravity. Certainly objects don't always accelerate with an acceleration of ##g## (after all, the force decreases as you get farther from the Earth), but when close to the surface, it is a good approximation to treat the gravitational field as a constant.

If the sheet is finite, then at far distances, it will look like a point charge. Then you can imagine what the formula will look like, however, from searching around, it is very difficult to get a closed form solution for a finite sheet of charge, hence the infinite sheet approximation.
Thank you.
 
axmls said:
IIf the sheet is finite, then at far distances, it will look like a point charge. Then you can imagine what the formula will look like, however, from searching around, it is very difficult to get a closed form solution for a finite sheet of charge, hence the infinite sheet approximation.
If the sheet is a finite disc, and the particle lies on the axis of the disc, the math for the field (multiply by charge of particle in the field to get the force) is shown here:

http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/electric/elelin.html#c3
 
Last edited by a moderator:
rcgldr said:
If the sheet is a finite disc, the math for the field (multiply by charge of particle in the field to get the force) is shown here:

http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/electric/elelin.html#c3

Ah, of course. My brain instantly jumped to a finite rectangular sheet. Yes, a disc has a very simple closed form along the axis through its center, and I'm sure the OP can confirm that we obtain the formula for an infinite sheet if we let the radius go to infinity.
 
Last edited by a moderator:
It the sheet is a rectangle and the particle lies on the central "axis" of the sheet, the sheet could be considered as an infinite number of lines of finite length, where the component of force perpendicular to the lines cancel, so only the component related to z needs to be considered. This is the math for a line, the math for a sheet would involve an integral based on the formula for a line:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html
 

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