Calculating Electric Field with Point Charge and Hollow Sphere

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Discussion Overview

The discussion revolves around calculating the electric field produced by a point charge placed near a perfectly conducting hollow sphere. Participants explore the implications of charge distribution and field behavior both inside and outside the sphere, addressing theoretical and conceptual aspects of electrostatics.

Discussion Character

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

Main Points Raised

  • One participant suggests treating the point charge as if it were at the center of the sphere to derive the electric field, E = Q/(4 π ε₀ D²), but another challenges this assumption due to the loss of symmetry when the charge is offset.
  • Another participant explains that the point charge induces a charge (-Q) on the inner surface of the sphere, which cancels the electric field inside the conductor, while the remaining charge (Q) distributes uniformly on the outer surface.
  • A participant points out that the expression for the electric field outside the sphere is valid for r > R, correcting a potential misunderstanding about the formula used.
  • There is a discussion about the distribution of induced charges, with one participant asserting that the inner surface develops a negative charge to maintain zero electric field inside the conductor, while another clarifies that the -Q charge is indeed induced on the inner surface.
  • One participant expresses confusion about the question and seeks clarification on finding an expression for the electric field outside the sphere, indicating a lack of clarity in the initial query.
  • Another participant confirms that the electric field outside the sphere depends only on the total charge and not on the position of the charge Q within the sphere.
  • A participant acknowledges a misunderstanding regarding the placement of the charge and corrects their earlier statement about the charge's location.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement regarding the behavior of electric fields and charge distributions. While some points are clarified, there remains uncertainty about the implications of charge placement and the resulting electric field calculations.

Contextual Notes

Participants reference the "method of images" and discuss the implications of charge distribution without providing a definitive expression for the electric field outside the sphere. The discussion includes assumptions about charge symmetry and the effects of conductor properties that are not fully resolved.

Who May Find This Useful

Readers interested in electrostatics, charge distribution, and the behavior of electric fields in conductive materials may find this discussion relevant.

jimbo007
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if u have an uncharged,perfectly conducting hollow sphere of thickness t and radius R, and a point charge Q is placed a distance D from the centre of the sphere so that R-t>D, what would the electric field, E, be?
i just treated it the same as if Q was in the centre of the sphere and the electric field lines came perpendicular to the sphere and so

[tex]E=\frac{Q}{4 \pi \epsilon_{0}D^2}[/tex]

anyone got any better ideas?
 
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jimbo007 said:
if u have an uncharged,perfectly conducting hollow sphere of thickness t and radius R, and a point charge Q is placed a distance D from the centre of the sphere so that R-t>D, what would the electric field, E, be?
i just treated it the same as if Q was in the centre of the sphere and the electric field lines came perpendicular to the sphere and so

[tex]E=\frac{Q}{4 \pi \epsilon_{0}D^2}[/tex]

anyone got any better ideas?
There is no reason to assume that you can do that. One the charge is offset from the center you've changed he symmetry of the situation.

Pete
 
The point charge induces a charge (-Q) on the inner surface as to cancel the field inside the conductor. The remaining induced charge (Q) will distribute itself over the surface of the sphere.
I'm pretty certain it will spread uniformly so that the electric field you got is correct.
 
jimbo007 said:
[tex]E=\frac{Q}{4 \pi \epsilon_{0}D^2}[/tex]
I assume you meant to write:
[tex]E=\frac{Q}{4 \pi \epsilon_{0}r^2}[/tex]
That would be correct for the field for r > R. (r = 0 is the center of the sphere.)

See my answer here: https://www.physicsforums.com/showthread.php?t=37090
 
There is no electric field inside the conductor. The conductor accomplishes this by arranging a layer of charge in an appropriate distribution on the outer surface of the sphere with a total amount equal to -Q. The inner surface of the sphere therefore develops a negative charge deficit equal to this (+Q) and also distributed appropriately (since there is no field inside the conductor). This all results in a negative image charge somwhere below the surface of the sphere, not quite in the center, and not necessarily near the surface, and not necessarily equal to -Q. I don't remember what the expression is off the top of my head; sorry. Look up the "method of images."
 
lol, thanks for the responses guys, very much appreciated
but I'm still completely stumped by the question
just to make it clear i want to find an expression for the electric field outside the sphere (after reading my first post i didnt think my question was very clear)

thanks again
 
jimbo007 said:
lol, thanks for the responses guys, very much appreciated
but I'm still completely stumped by the question
just to make it clear i want to find an expression for the electric field outside the sphere (after reading my first post i didnt think my question was very clear)
What's stumping you? I gave the expression for the field outside the sphere in my first response. Now... to explain why that's the right answer requires a little more...
 
turin said:
There is no electric field inside the conductor.
Right.
The conductor accomplishes this by arranging a layer of charge in an appropriate distribution on the outer surface of the sphere with a total amount equal to -Q.
I believe you have it backwards. The -Q is induced on the inner surface. This surface charge is arranged to exactly cancel the field from the charge within the cavity, thus producing zero field everywhere inside the conductor.
 
i just typed out my response and realized something. i couldn't see the difference between the formula i gave and the formula u gave but now i think i see it.
so by the sounds of it, it doesn't matter where you place the charge Q inside the sphere, E outside the sphere depends on the position only from the centre of the sphere. is this right?
 
Last edited:
  • #10
That is correct.
 
  • #11
Doc Al,
Oops. I read the post too quickly. I was responding under the false impression that the point charge, Q, was placed outside the conductor. Sorry to all.
 

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