Gauss' Law & 2 Charged Cylinders

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Using Gauss' Law, the electric field between two concentric charged cylinders is determined without considering the charge on the outer cylinder, as long as the system maintains cylindrical symmetry. Grounding the outer cylinder ensures it is at zero potential, which influences the induced charge on it but does not alter the electric field between the cylinders. The outer cylinder's grounding means it has the same potential as infinity, leading to no electric field outside it. This grounding condition indicates that the outer cylinder must have an induced charge that balances the field created by the inner cylinder. Ultimately, the grounding of the outer cylinder simplifies the analysis of the electric field and potential in the space between the two cylinders.
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Hi, could someone offer some advice on the following problem:

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Q. Using Gauss' law, obtain expressions for the electric field and potential in the space between two thin, hollow, concentric conducting cylinders, of radii a and b, with the outer cylinder connected to earth
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I know that the E-field of the inner cylinder is E=Q/4piEoa^2 in the radial direction (if the cylinder has a charge of Q).

I also realize that if the outer cylinder was not connected to earth, it's just a capacitor.

However, I'm really confused as to what affect the earthing of the outer cylinder has on the electric field and potential in between the two cylinders!

Thanks
 
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Suprisingly none. When you use Gauss's law to find the field between the cylinders, you make no reference to the charge outside the gaussian surface. Of course, this is only valid if whatever is out there is cylindrically symmetrical. The only thing that grounding the outer plate does is that it is at potential 0. What does this mean about the field outside the outer cylinder (if it is at the same potential as infinity)? This can tell you what charge has been induced on the outer cylinder.
 
StatusX said:
The only thing that grounding the outer plate does is that it is at potential 0. What does this mean about the field outside the outer cylinder (if it is at the same potential as infinity)? This can tell you what charge has been induced on the outer cylinder.

So the external cylinder produces no electric field outside and thus must have the opposite potential to the inner cylinder?
 
It produces an electric field that puts it at zero potential, which means it is at the same potential as infinity. Basically what you said, switching the words "potential" and "field."
 
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