E & M, Infinite sheet of charge

In summary: The change 'at' the surface' must be 4(pi)s, if he said 'across' the surface, I would have been convinced by the same argument you are giving me now long before.
  • #1
SpaceExplorer
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The problem I have is about a simple remark made in the book 'Berkeley Physics Course Volume 2, Electricity and Magnetism', chap. 3 figure 3.4 b. It says that if we have an infinite sheet of charge but with 'other charges' present elsewhere in the system, the only thing we can predict is that at the surface, there will be a change of 4(pi)s, where 's' is the surface charge density, in Ex and 0 in Ey. Why is that? (the book only deals in m.k.s units)
 
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  • #2
SpaceExplorer said:
Why is that?
Consider the field from an infinite sheet of charge with nothing else around. What's the field on each side? Then consider the additional field that might be present because of other charges. Apply the principle of superposition.

SpaceExplorer said:
(the book only deals in m.k.s units)
Purcell uses (if I recall) Gaussian CGS units, not S.I. (mks) units.
 
  • #3
Oh... I wanted to write C.G.S, but wrote M.K.S instead, thanks for pointing that out. The problem with the superposition thing is that the scenario doesn't consider a particular arrangement of external charges, but rather generalises the proposition to all the possible arrangements; logically, the change in the field at a point on the surface should be different for different arrangements, so it doesn't make sense that the end result will always have to be 4.(pi).s. Moreover there's no variable or constant in the final result that even accounts for the presence of extra charges, 's' is just the surface charge density, while 4 and pi are unrelated constants.
 
  • #4
SpaceExplorer said:
The problem with the superposition thing is that the scenario doesn't consider a particular arrangement of external charges, but rather generalises the proposition to all the possible arrangements;
That's the beauty of the superposition argument, not the problem.

SpaceExplorer said:
logically, the change in the field at a point on the surface should be different for different arrangements,
Why is that?

The idea is this. Say there are a bunch of charges in arbitrary arrangement (but just not on the sheet) that end up creating a field E where that sheet of charge is to be located. To find the total field, you would add to that the field from the sheet of charge. So on one side you'd have ##E - 2\pi\sigma## and on the other side you'd have ##E + 2\pi\sigma##, for a difference of ##4\pi\sigma##.
 
  • #5
I think you're right.I thought of the same thing at the beginning. But I think the author has done a technical mistake because of which I was having the trouble. Purcell says 'the change 'at' the surface' must be 4(pi)s, if he said 'across' the surface, I would have been convinced by the same argument you are giving me now long before.
 

1. What is an infinite sheet of charge?

An infinite sheet of charge is a theoretical construct used in electrostatics to represent a surface with a uniform charge density that extends infinitely in all directions. It is often used as a simplified model to study the behavior of electric fields and forces.

2. How is the electric field calculated for an infinite sheet of charge?

The electric field for an infinite sheet of charge can be calculated using the formula E = σ/2ε0, where σ is the surface charge density and ε0 is the permittivity of free space. This formula holds true at all points above or below the sheet, regardless of distance from the sheet.

3. What is the direction of the electric field for an infinite sheet of charge?

The electric field for an infinite sheet of charge is always perpendicular to the surface of the sheet. This means that the electric field lines are parallel and evenly spaced, pointing away from the sheet on one side and towards the sheet on the other side.

4. How does the electric field change with distance from an infinite sheet of charge?

The electric field for an infinite sheet of charge does not change with distance from the sheet. This is because the sheet has an infinite extent in all directions, so the electric field is the same at all points above or below the sheet.

5. Can an infinite sheet of charge exist in real life?

No, an infinite sheet of charge is a theoretical concept and cannot exist in real life. However, it is a useful model for understanding the behavior of electric fields and forces in certain situations, such as in parallel plate capacitors.

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