Electric Field Inside Cylindrical Capacitor

In summary, the conversation discusses the use of the relation between flux, electric field, and charge to calculate the electric field inside a cylindrical capacitor. The integral simplifies to E * A = (q_enclosed)/(ε_naught) when using a cylindrical gaussian surface. The question then addresses the potential impact of negative charges on the outside cylinder and whether they should be considered in the calculation of the electric field. The response explains that the electric flux through the gaussian surface accounts for all field lines, including those produced by the negative charges, and considering them separately would result in double-counting. The conversation ends with a question about the magnitude of the electric field produced by the outer charge inside the cylindrical shell.
  • #1
Homework Statement
When we want to find the electric field inside of a cylindrical capacitor, we can use Gauss's law and the relation between flux and field to calculate what this field is.
Relevant Equations
Gauss's law
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we know that flux is equal to the area integral of electric field dotted with dA and we can set this equal to charge enclosed divided by epsilon naught. Thus, in this case, the integral simplifies to E * A = (q_enclosed)/(ε_naught) when we choose a cylindrical gaussian surface with radius of r.

My question, then, is why are we allowed to use this relation to find electric field inside of the capacitor. I thought that the electric field that is calculated only describes the electric field that the charges enclosed produce. In this situation, wouldn't the negative charges on the outside cylinder affect the Electric Field too? If it does, the electric field that we find wouldn't be the right electric field between the cylinders. Is there a reason that we can ignore the negative charge on the outside cylinder in this capacitor? Or is my thought process incorrect?
 
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  • #2
Look at the drawing on the right. Whatever field lines leave the inner surface where the positive charges are located terminate at the inner surface of the outer cylinder where the negative charges are. The electric flux through the dotted Gaussian surface essentially counts all the electric field lines. If you were to somehow account for the charges outside the Gaussian surface, you will be double-counting.
 
  • #3
@OP. What do you think is the magnitude of the field produced by the outer charge inside the cylindrical shell?
 

1. What is an electric field inside a cylindrical capacitor?

The electric field inside a cylindrical capacitor refers to the strength and direction of the electric force present between the two conducting plates within the capacitor.

2. How is the electric field calculated inside a cylindrical capacitor?

The electric field inside a cylindrical capacitor can be calculated using the formula E = V/d, where E is the electric field, V is the potential difference between the plates, and d is the distance between the plates.

3. Does the electric field inside a cylindrical capacitor vary?

Yes, the electric field inside a cylindrical capacitor varies depending on the distance from the center of the capacitor. The electric field is strongest at the edges of the plates and weaker towards the center.

4. How does the dielectric material affect the electric field inside a cylindrical capacitor?

The dielectric material between the plates of a cylindrical capacitor can decrease the strength of the electric field by reducing the potential difference between the plates. This is due to the dielectric material's ability to store electric charge and decrease the overall capacitance of the capacitor.

5. What factors can affect the electric field inside a cylindrical capacitor?

The electric field inside a cylindrical capacitor can be affected by factors such as the distance between the plates, the potential difference between the plates, the type of dielectric material used, and the shape and size of the plates.

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