Still more problems with Gauss Law

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Homework Help Overview

The discussion revolves around applying Gauss's Law to determine the electric field at two points related to a spherical cavity with a charge at its center within a metal object. The problem involves understanding the implications of charge distribution and the use of Gaussian surfaces in different regions.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply Gauss's Law to find the electric field at two points, questioning the appropriateness of using a spherical Gaussian surface for point P2 located within the metal. Some participants discuss the need to consider induced charges and the implications of charge enclosure.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of how to apply Gauss's Law in this context. Some guidance has been offered regarding the necessity of accounting for induced charges on the metal's inner surface, but no consensus has been reached on the specific approach for point P2.

Contextual Notes

There is uncertainty regarding the charge distribution within the metal and how it affects the application of Gauss's Law. The original poster is also unsure about the implications of using a spherical surface for point P2, highlighting a need for clarification on induced charges.

stunner5000pt
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Ok I'm realllly unsure about this!

If a spherical cavity of radius 3.66cm in a piece of metal (kind of cube, but not a perfect cube) has a charge of +Q at it's centre and there is a point P1 located half way between the spherical cavity and it's surface and a point P2 located in the metal piece , use gauss Law to find the electric field at
a) Point P1
b) point P2

a) This is fine for me

Let e0 = permittivity of free space epsilon 0

e0 SurfaceIntegral (E dA) = q
e0 E (4 pi r^2 ) = q
E = kq /r^2
which is coulomb's law derived! and just plug and away i go!

b) But for point P2

err can i actually use a spherical surface here??

as in do the same thing as before but use a bigger value for r i.e. radius of sphere + distance of sphere to point P2

appropriate? or not?
 
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Umm...the answer to that would be : NOT YET. Mostly because you don't yet know what charges are enclosed by this Gaussian surface.

Read what your text has to say about induced charges and electric fields inside a piece of metal.
 
You can still use a spherical surface though.

Claude.
 
Claude Bile said:
You can still use a spherical surface though.

Claude.


i'm not quite sure how i would use it , so the shere would have a radius of 3.66cm + A ??

e0 E 4 pi (3.66+A)^2 = 126 x 10^-9

something liek this??
 
You need to take into account the induced charges on the inner surface of the metal.

Claude.
 

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