Charged Plate w/ Gaussian Cylinder: Integral E*dA

Thread starter Idividebyzero
Start date Jun 17, 2011
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Cylinder Gaussian

In summary, a charged plate with Gaussian cylinder is an idealized model used in electrostatics to study the behavior of electric fields. The electric field for this model can be calculated using Gauss's law, with the Gaussian cylinder serving as a convenient closed surface. While this model has practical applications in understanding electric fields, it also has limitations such as assuming infinite dimensions and uniform charge distribution. It is important to use this model with caution and consider its limitations when applying it to real-world situations.

Jun 17, 2011

Idividebyzero

1. Consider a uniformly charged conducting
plate with an infinite extent, where the sur-
face charge density is surf . We introduce a
Gaussian surface as a cylindrical pillbox of ra-
dius a, half-way submerged into the surface.
The figure below shows a chunk of the infinite
plate and the pillbox configuration.

2. integral E * dA

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Jun 17, 2011

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Well, what's your answer?

1. What is a charged plate with Gaussian cylinder?

A charged plate with Gaussian cylinder is an idealized model used in electrostatics to study the behavior of electric fields. It consists of a uniformly charged flat plate with a circular cylinder placed above it, both with infinite dimensions. This model is often used to calculate the electric field and potential at a point in space.

2. How is the electric field calculated for a charged plate with Gaussian cylinder?

The electric field for a charged plate with Gaussian cylinder can be calculated using the integral form of Gauss's law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of the medium. In this case, the surface is the Gaussian cylinder and the enclosed charge is the charge on the plate.

3. What is the significance of the Gaussian cylinder in this model?

The Gaussian cylinder serves as a convenient closed surface to apply Gauss's law and calculate the electric field. Since the electric field is constant and perpendicular to the surface of the plate, the electric flux through the curved surface of the cylinder is the same as the flux through the flat surface of the plate. This simplifies the calculation of the electric field.

4. Does a charged plate with Gaussian cylinder have any real-world applications?

While this model is an idealization and does not accurately represent any physical system, it can be used to understand and analyze the behavior of electric fields in various situations. For example, it can be used to study the behavior of parallel plate capacitors, which have practical applications in electronic devices.

5. Are there any limitations to the charged plate with Gaussian cylinder model?

Yes, there are some limitations to this model. It assumes an infinitely large plate and cylinder, which is not possible in reality. It also assumes a constant and uniform charge distribution, which may not be the case in some systems. Additionally, it only considers electrostatics and does not take into account any dynamic effects such as induced currents. Therefore, it is important to use this model with caution and consider its limitations when applying it to real-world situations.