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Help with an electrostatics problem

  • #1
question: A positive charge exists in free space.Now, the charge is enclosed by a spherical shell of finite thickness.What effect does it have on the field lines emanating from the charge.

answer:The field lines emanate outwards from the charge till they reach the inner surface of the shell after which they continue from the outer surface. The field lines do not exist over the thickness of the shell.

query:Why should the field lines not exist over the thickness of the shell?
 

Answers and Replies

  • #2
UltrafastPED
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If the shell is a conducting sphere:
(1) electrons move within the conductor to the inner surface so as to cancel the enclosed positive charge.
Every field line has been terminated.
(2) the electrons that moved to the inner surface left a net positive charge at the outer surface. These will be evenly spaced (because electrons move so as to minimize local charges).
This creates new field lines (to infinity) that are spherically symmetrical ... even if the original positive charge was not.

And there are no field lines inside the conducting shell.
 
  • #3
I understand your point. If i draw a Gaussian surface arbitrarily close to the outer surface of the shell ( in between the the two surfaces), it will enclose no net charge hence no flux and no field lines either. However, is it not true that their is a positive charge at the center of the shell and induced negative charge on the inner surface? So shouldn't there be field lines originating from positive charge and terminating on the negative charge just like that between the plates of a parallel plates capacitor which are oppositely charged?
 
  • #4
ehild
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question: A positive charge exists in free space.Now, the charge is enclosed by a spherical shell of finite thickness.What effect does it have on the field lines emanating from the charge.
answer:The field lines emanate outwards from the charge till they reach the inner surface of the shell after which they continue from the outer surface. The field lines do not exist over the thickness of the shell.

query:Why should the field lines not exist over the thickness of the shell?
It was not specified if the shell is a conductor or a dielectrics (insulator).

In case of a dielectric shell, the electric field is not zero inside the shell, but different from that inside the cavity, as the inner charge polarizes the dielectrics and some of the field lines continue in dipole chains.

If it is a metal shell, you know that there can not exist static electric field in the metal. If there was some field, it would drive the free electrons till they reach the surface. There is surface charge at both sides of a metal layer, and the net charge on both surfaces are of equal magnitude and opposite sign.

ehild
 
  • #5
ehild
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I understand your point. If i draw a Gaussian surface arbitrarily close to the outer surface of the shell ( in between the the two surfaces), it will enclose no net charge hence no flux and no field lines either. However, is it not true that their is a positive charge at the center of the shell and induced negative charge on the inner surface? So shouldn't there be field lines originating from positive charge and terminating on the negative charge just like that between the plates of a parallel plates capacitor which are oppositely charged?
The induced negative charge is equal in magnitude to the positive charge at the centre. The number of field lines emerging from a positive charge or ending in a negative charge q is q/ε. So all field lines emerging from the central charge end at the surface charges on the inner surface on the shell.
As the shell was neutral, a positive surface charge appear on the outer surface, equal in magnitude with the inner charge.
In case of a capacitor, there are two plates, and opposite surface charges q and -q on the inner surfaces. There is air or some dielectrics between the plates, and the number of the electric field lines is q/ε.
 
  • #6
You said,"all field lines emerging from the central charge end at the surface charges on the inner surface on the shell". Does that mean the electric field vanishes with the termination of field lines?
 
  • #7
ehild
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The field lines represent the electric field, and the electric field is proportional with the density of the field lines.
You can say that the electric field lines terminate at the surface charges, as the electric field is zero inside the metal.

ehild
 
  • #8
OK i seem to be getting it. But following the same argument can't we conclude that there is no electric field in between the capacitor plates?(since there too the lines terminate at the negative plate). Or is it that the dielectric makes a difference? If so, how exactly? Help will be appreciated..
 
  • #9
ehild
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In case of a capacitor, the field lines are between the plates. The surface charges are on the inner surfaces. The field lines emerge from the positive charges and terminate on the negative ones. No field lines are present inside the metal plates or outside the capacitor.

ehild
 

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  • #10
OK! thank you.
 
  • #11
ehild
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You are welcome.

ehild
 
  • #12
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Dear All

I planned to give electrostatic induction to the abrasive grain (Di electric) to get attracted by the positive charged plate, where i have kept sticky pad, so that the abrasive grains are attracted & deposited.

The size of abrasive grains are : 60 grit size. ( Kept at Negative Plate)
The Size of sticky pad is: 1 mtr x 1 mtr. (Kept at Postive Plate)

Can you please tell me the following:

1 . Amount of Electrical energy has to be applied in Positive & negative plates.

2. Nature of Metal which i have to use to design positive & negative plates and its thickness?

Your guidance will help me a lot
 
  • #13
ehild
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Hi Kiran, welcome to PF.

I can not answer your question. And this is a forum for homework problems. Try to send your question to one of the Engineering forums, like Materials and Chemical Engineering.

ehild
 

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