Electric fields and a spherical surface

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Discussion Overview

The discussion revolves around the behavior of electric fields in relation to a point charge at the center of a conducting spherical surface, particularly when the surface is connected to the Earth. Participants explore concepts of charge distribution, polarization, and the implications of grounding on electric fields.

Discussion Character

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

Main Points Raised

  • One participant questions why the electric field outside a conducting spherical surface becomes zero when it is connected to the Earth, suggesting that the surface acquires a charge of -Q.
  • Another participant discusses the effect of a central charge on the mixed positive and negative charges in the shell, particularly if the shell is not earthed initially.
  • There is a proposal that the surface becomes polarized, with negative charges on the inner side and positive charges on the outer side, but this does not affect the electric field outside the surface when earthed.
  • Concerns are raised about the concept of zero thickness in the context of charge distribution on the surface, with a suggestion that charges can be thought of as being located just inside and outside the sphere.
  • A participant mentions Gauss's Law as a method to find the surface charge that ensures the electric field inside the conducting shell is zero.
  • Another participant references electrostatic induction, noting that the induced charge has the same magnitude as the inducing charge but with an opposite sign.

Areas of Agreement / Disagreement

Participants express various viewpoints on the behavior of charges and electric fields, with no clear consensus reached on the implications of grounding or the specifics of charge distribution.

Contextual Notes

Participants discuss the idealization of zero thickness for the conducting surface and the implications of this assumption on charge placement and electric field behavior. The discussion includes unresolved questions about the calculations for induced charge values.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics, particularly those exploring electrostatics, charge distribution, and the effects of grounding on electric fields.

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If there's a point charge Q at the center of a spherical surface(of radius a) made of conducting material that is connected to earth, why is the electric field past r>a zero ?

Doesn't it imply that the spherical surface becomes charged with -Q ? And why is that?

What would be the difference if the spherical surface wasn't connected to the Earth ?
 
Last edited:
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A neutral objects contains an even mix of both positive and negative charge.
What does the central charge do to those mixed charges in the shell (assume the shell is not earthed to start with)?

When a conductor is earthed, any excess charge free to move will be drained away.
 
I would say that the surface becomes polarized ( -charges at the inner side and +charges at the outer side), that would make no difference to the electric field outside the surface, however, when the surface is connected to earth, the electric field outside becomes zero. Does that means that the +charges in the surface are drained away because they are being repelled by the center charge, and the -charges stay because they are being attracted ?

I said that the surface becomes polarized but since it's a surface it has no thickness,i.e:charges can't really be placed on the inner side or outer side. So if there was no connection to Earth how would the charges on the surface place them self?
 
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There is no such thing as zero thickness - that is an idealization.
If you like, you can think of the charges being pulled to positions infinitesimally just inside and outside the sphere.

But you have answered your own questions - well done.
 
Simon Bridge said:
There is no such thing as zero thickness - that is an idealization.
If you like, you can think of the charges being pulled to positions infinitesimally just inside and outside the sphere.

But you have answered your own questions - well done.


One last question, we assumed that the surface got charged with -Q. Is that value calculated by any equation? If so, what equations can I use?
 
Last edited:
Gausses Law.

Find the surface charge that makes the electric field inside the conducting shell zero.
 
I just read about electrostatic induction and it seems that the induced charge as the same value as the inducting charge, but with opposite sign.

And thanks the replys.
 
That's right ... and the earlier replies tell you why that is, and tells you how to work out how the induced charge is distributed.
 

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