Type(s) of charge distribution for spherical and cylindrical gaussian surfaces

In summary, a Gaussian surface is an imaginary surface used in Gauss's law to calculate the electric field due to a charge distribution. There are two types of Gaussian surfaces: spherical and cylindrical. The choice of which surface to use depends on the symmetry of the charge distribution. The charge distribution on a spherical Gaussian surface is directly proportional to the electric field, as described by Gauss's law. A Gaussian surface can be used for both uniform and non-uniform charge distributions, but calculations become more complex for non-uniform distributions. The charge distribution on a cylindrical Gaussian surface differs from a spherical Gaussian surface because it is not uniform, resulting in a non-uniform electric field on the surface.
  • #1
yanyin
21
0
I have a new question:
"In applying Gauss's Law describe the types(s) of charge distribution for which (a) a spherical gaussian surface is useful and (b) a cylindrical gaussian surface is useful"
please help!
 
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  • #2
Seems pretty obvious. Use a Spherical surface for objects with spherical symmetry and cylindrical surface for objects with a cylindrical symmetry.
 
  • #3


In applying Gauss's Law, the type(s) of charge distribution for which a spherical gaussian surface is useful are spherically symmetric charge distributions. This means that the charge is distributed equally in all directions around a central point. Examples of this type of charge distribution include a point charge, a charged sphere, or a charged shell.

On the other hand, a cylindrical gaussian surface is useful for charge distributions that have cylindrical symmetry. This means that the charge is distributed evenly around a central axis, but not necessarily in all directions. Examples of this type of charge distribution include a long charged wire or a charged cylinder.

In both cases, the gaussian surface is chosen because it simplifies the calculation of the electric field and allows us to apply Gauss's Law. The spherical gaussian surface is useful because it allows us to take advantage of the symmetry of the charge distribution, while the cylindrical gaussian surface is useful for charge distributions that have a cylindrical shape.

In summary, the choice of gaussian surface depends on the symmetry of the charge distribution being studied. A spherical gaussian surface is useful for spherically symmetric charge distributions, while a cylindrical gaussian surface is useful for charge distributions with cylindrical symmetry.
 

1. What is a Gaussian surface?

A Gaussian surface is an imaginary surface used in Gauss's law to calculate the electric field due to a charge distribution. It is an arbitrary closed surface that encloses the charge distribution and allows for the simplification of calculations.

2. What is the difference between a spherical and cylindrical Gaussian surface?

A spherical Gaussian surface is a closed surface in the shape of a sphere, while a cylindrical Gaussian surface is a closed surface in the shape of a cylinder. The choice of which surface to use depends on the symmetry of the charge distribution.

3. How is the charge distribution on a spherical Gaussian surface related to the electric field?

The charge distribution on a spherical Gaussian surface is directly proportional to the electric field at any point on the surface. This relationship is described by Gauss's law, which states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space.

4. Can a Gaussian surface be used for non-uniform charge distributions?

Yes, a Gaussian surface can be used for both uniform and non-uniform charge distributions. However, the calculations become more complex for non-uniform distributions as the electric field may vary at different points on the surface.

5. How does the charge distribution on a cylindrical Gaussian surface differ from a spherical Gaussian surface?

The charge distribution on a cylindrical Gaussian surface is not uniform like on a spherical Gaussian surface. This is because the charge is distributed along the curved surface of the cylinder, resulting in a non-uniform electric field on the surface.

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