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A point charge Q is inside a cavity in an uncharged conductor. Is the force on Q necessarily zero?

The explanation in the answer goes as

No. For example, if it is very close to the wall, it will induce a charge of the opposite sign on the wall, and it will be attracted.

This sounds weird to me because:-

  1. First of all, it says if Q is very close to the wall, it will induce a charge of the opposite sign on the wall but opposite sign shall develop every time on the inner surface of cavity irrespective of the particle's position inside the cavity.

  2. Isn't it that getting attracted would signify experiencing a force because of charge's own field since the field inside the cavity is just because of the charge placed [BY GAUSS LAW].

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  • $\begingroup$ "Is the force on Q necessarily zero?" Due to what the force are you saying?is it the induced charge or any other charge outside the conductor? $\endgroup$ – user212727 Jan 30 at 13:35
  • $\begingroup$ @TheBroly I have provided both question and answer as they are presented before me by the book. First of all, I guess worrying about external charges isn't worth since they shall pay no contribution to the field inside the cavity [hence no contribution to force on Q inside cavity as well]. Secondly, the Instructor's solution manual states that the force may be experienced due to induced charges if Q is placed very near to cavity wall! $\endgroup$ – Onkar Singh Jan 30 at 14:15
  • $\begingroup$ I think answer in physics.stackexchange.com/questions/356444/… may help $\endgroup$ – user212727 Jan 30 at 14:18
  • $\begingroup$ @TheBroly Also tell me, if I provide a link to the book [its Griffith's], will it go against the community's guidelines? I mean can someone claim I'm letting others avail a soft copy of books which otherwise are purchased? $\endgroup$ – Onkar Singh Jan 30 at 14:18
  • $\begingroup$ If there is any page you want to show,you can send the link of picture of that page $\endgroup$ – user212727 Jan 30 at 15:01
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First of all, it says if Q is very close to the wall, it will induce a charge of the opposite sign on the wall but opposite sign shall develop every time on the inner surface of cavity irrespective of the particle's position inside the cavity.

Yes, the presence of the charge Q will always induce charges of the opposite sign on the inner wall (field inside the conductor should be zero and thus, Gauss law tells us that the inner surface must have a total of -Q charge). However, if the charge is placed exactly at the centre, the charge distribution over the inner surface is symmetric, so there is no force on the charge. But in all other cases, the charge will experience a force due to the induced charges on the inner surface.

Isn't it that getting attracted would signify experiencing a force because of charge's own field since the field inside the cavity is just because of the charge placed [BY GAUSS LAW].

  • Firstly, field as calculated by Gauss law is due to all the charges, not just the ones enclosed by the closed surface over which we apply Gauss law.
  • The induced charges are exerting a force on Q. As far as i know, a charge does not exert a force on itself.
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