Field inside a cavity inside a conductor

In summary, the conversation discussed the properties of a conductor and the first Uniqueness theorem, with the conclusion that the field inside a cavity within a conductor is zero. However, it was questioned whether this result would still hold if point charges were placed inside the cavity. It was argued that Laplace's equation would not be satisfied everywhere, making the first uniqueness theorem invalid. However, the other person disagreed and pointed out that Poisson's equation still takes into consideration the charge distribution and satisfies the uniqueness theorems. It was then clarified that while the uniqueness theorem still holds, the potential inside the conductor will not be constant. Finally, it was noted that following the properties of a conductor is important for the system to exist, as per Earn
  • #1
Kolahal Bhattacharya
135
1
In the context of properties of conductor & 1st Uniqueness theorem, Griffiths proves that field inside a cavity( empty of charge) within a conductor is 0.
Is the result same if we place a +q & a -q (so that Q(enc)=0)
suspended in air inside the cavity?
 
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  • #2
I would say no, because Laplace's equation won't be satisfied everywhere, because of the point charges. So you can't apply the first uniqueness theorem.
 
  • #3
I agree with you about the result but cannot be satisfied with your argument.As Poisson's eqn. takes into consideration Rho(r)...& still satisfies Uniqueness theorems. Lastly I think it is solved:we will have a unique V(r) function from which E follows.This V(r) will not satisfy properti--es of Laplace eqn.In boundary, V(r)=V(0),Following properties of a conductor...Otherwise the system I'm talking of will not exist at all.It will collapse immediately after we place them together within the cavity,following Earnshaw's theorem.Any conceptual mistake?Please help!
 
  • #4
Yeah, you're right, the uniqueness theorem still holds and the potential can be uniquely determined, but it won't be constant inside the conductor.

Also, I don't understand why you say V(R) = V(0)?
 
Last edited:

1. What is a "field inside a cavity inside a conductor"?

The term "field inside a cavity inside a conductor" refers to the electric field present within a hollow space or cavity that is enclosed by a conducting material. The conducting material acts as a barrier, confining the electric field to the inside of the cavity.

2. Why is the electric field inside a cavity inside a conductor zero?

The electric field inside a cavity inside a conductor is zero because any external electric field that is applied to the conductor will induce an equal and opposite electric field within the conductor. This induced electric field cancels out the external field inside the conductor, including within the cavity.

3. How does the shape and size of the cavity affect the electric field inside a conductor?

The shape and size of the cavity can affect the electric field inside a conductor by influencing the distribution of charges on the surface of the conductor. In general, a larger cavity will result in a weaker electric field inside the conductor, while a smaller cavity may result in a stronger electric field.

4. Is the electric field inside a cavity inside a conductor affected by the material of the conductor?

No, the electric field inside a cavity inside a conductor is not affected by the material of the conductor. As long as the conductor is a perfect conductor (meaning it has no resistance), the electric field inside the cavity will remain zero regardless of the material it is made of.

5. Can the electric field inside a cavity inside a conductor ever be non-zero?

Yes, the electric field inside a cavity inside a conductor can be non-zero if the conductor is not a perfect conductor. In this case, there will be some internal resistance in the conductor, which can result in a non-zero electric field inside the cavity under certain conditions.

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