Still more problems with Gauss Law

AI Thread Summary
The discussion revolves around applying Gauss's Law to find the electric field at two points related to a spherical cavity with a charge at its center. For point P1, the calculations align with Coulomb's law, allowing for straightforward application of Gauss's Law. However, for point P2, there is uncertainty about using a spherical Gaussian surface, as the enclosed charge must be determined first. The conversation highlights the importance of considering induced charges on the inner surface of the metal when calculating the electric field in such scenarios. Understanding these concepts is crucial for correctly applying Gauss's Law in electrostatics.
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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