# Gauss' Law & 2 Charged Cylinders

• Hoofbeat
In summary, The use of Gauss' law allows for the determination of the electric field and potential between two concentric conducting cylinders, with the outer cylinder connected to earth. The presence of earth grounding the outer cylinder does not have any effect on the electric field, as the calculation of the field between the cylinders does not take into account the charge outside the Gaussian surface. However, grounding the outer cylinder does mean that it is at potential 0 and has no electric field outside, indicating that it is at the same potential as infinity. This allows for the determination of the charge induced on the outer cylinder.
Hoofbeat
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

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."

## 1. What is Gauss' Law?

Gauss' Law is a fundamental law in physics that relates the electric field to the distribution of electric charges. It states that the electric flux through a closed surface is proportional to the total charge enclosed by that surface.

## 2. How do you apply Gauss' Law to two charged cylinders?

To apply Gauss' Law to two charged cylinders, we first need to identify the closed surface that encloses both cylinders. This can be done by drawing a Gaussian surface around both cylinders. Then, we calculate the total charge enclosed by the surface and use this value to calculate the electric flux through the surface. Finally, we equate the electric flux to the charge enclosed to determine the electric field at any point on the surface.

## 3. Can Gauss' Law be used to calculate the electric field inside the cylinders?

Yes, Gauss' Law can be used to calculate the electric field inside the cylinders. To do so, we just need to draw a Gaussian surface inside the cylinders and follow the same steps as mentioned in the previous question.

## 4. Is Gauss' Law affected by the shape of the charged cylinders?

No, Gauss' Law is not affected by the shape of the charged cylinders. As long as the closed surface encloses the cylinders and the charge enclosed is known, the electric field can be calculated using Gauss' Law regardless of the shape of the cylinders.

## 5. Can Gauss' Law be applied to more than two charged cylinders?

Yes, Gauss' Law can be applied to any number of charged cylinders. The same steps mentioned earlier can be followed where a closed surface is drawn around all the cylinders and the total charge enclosed is used to calculate the electric field at any point on the surface.

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