Calculating E Field Inside Cylinder of Finite Height

In summary, the conversation discusses the calculation of the E field inside a cylinder with a uniform charge density. While for an infinitely long cylinder, the field can only point radially outward, leading to a field of zero everywhere according to Gauss's law, the field can depend on the height in this case. However, it cannot depend on the angular coordinate.
  • #1
Fibo112
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I have a cylinder with radius r and height h and a uniform charge density. Now I am supposed to calculate the E field inside the cylinder. If the cylinder was infinitely long the symmetry would dictate that the field can only point radially outward, so gausses law would give me a field of zero everywhere. In the solutions it uses the argument that the field only depends on the radius due to symmetry. But in this case the cylinder is not infinite, so why can't the field depend on the height?
 
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  • #2
Fibo112 said:
I have a cylinder with radius r and height h and a uniform charge density. Now I am supposed to calculate the E field inside the cylinder. If the cylinder was infinitely long the symmetry would dictate that the field can only point radially outward, so gausses law would give me a field of zero everywhere. In the solutions it uses the argument that the field only depends on the radius due to symmetry. But in this case the cylinder is not infinite, so why can't the field depend on the height?
It can depend on height. In this case it can not depend on the angular coordinate.
 
Last edited:

1. How do you calculate the electric field inside a cylinder of finite height?

The electric field inside a cylinder of finite height can be calculated using the formula E = λ/2πεr, where λ is the linear charge density, ε is the permittivity of the material, and r is the distance from the center of the cylinder.

2. What is the significance of the finite height in the calculation of electric field inside a cylinder?

The finite height of the cylinder affects the distribution of charge and therefore, the electric field inside the cylinder. It is an important factor to consider when calculating the electric field.

3. Can the electric field inside a cylinder of finite height be uniform?

No, the electric field inside a cylinder of finite height is not uniform. The electric field strength varies depending on the distance from the center of the cylinder and the height of the cylinder.

4. How does the electric field inside a cylinder of finite height differ from that of an infinite cylinder?

Unlike an infinite cylinder where the electric field is constant at all points, the electric field inside a cylinder of finite height decreases as the distance from the center of the cylinder increases. Additionally, the finite height of the cylinder also affects the distribution of charge and the electric field strength.

5. What factors affect the calculation of electric field inside a cylinder of finite height?

The calculation of electric field inside a cylinder of finite height is affected by factors such as the linear charge density, the permittivity of the material, the radius of the cylinder, and the height of the cylinder. Additionally, the distribution of charge and the distance from the center of the cylinder also impact the calculation.

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