Electric Field Inside a Cylindrical Gaussian Surface: Exploiting Symmetry

In summary, when considering a cylindrical Gaussian surface with the same geometrical axis as an infinitely long cylinder, the flux through the closed surface can be used to find the electric field inside. This can be done by exploiting symmetry and ignoring some parts of the Gaussian surface, regardless of the infinite nature of the cylinder. This method can be used to find the electric field inside a cylindrical Gaussian surface in terms of volume charge density and charge configuration.
  • #1
jaejoon89
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What is the electric field inside a cylindrical Gaussian surface in terms of volume charge density?
 
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  • #2
What is the charge configuration ie. how are the charges distributed? Or are you referring to [tex]\nabla \cdot \mathbf{D} = p_V[/tex]?
 
  • #3
I'm not familiar with that notation (the upside down triangle). I was given volume charge density and needed to find the electric field inside an infinitly long cylinder. I know rho (vol. charge density) = Q/V but don't know what to use for the volume, since it's infinite.
 
  • #4
Okay, then in that case just ignore the notation above. Now, exploit symmetry here. Do this by considering a cylindrical Gaussian surface in the cylinder with the same geometrical axis. How do you find the flux through the closed surface and hence the field? Never mind if it's infinite. That is just a hint to ignore some parts of the Gaussian surface.
 

FAQ: Electric Field Inside a Cylindrical Gaussian Surface: Exploiting Symmetry

1. What is a Gaussian surface?

A Gaussian surface is an imaginary surface that is used in Gauss's Law to calculate the electric field of a charge distribution. It is typically chosen to be a symmetrical shape, such as a sphere, cylinder, or cube, to simplify the calculations.

2. How is a Gaussian surface different from a regular surface?

A Gaussian surface is an imaginary surface that is used for mathematical calculations, while a regular surface is a physical boundary or boundary between different materials.

3. How do you choose a Gaussian surface for a given problem?

The choice of Gaussian surface depends on the symmetry of the charge distribution. It should be chosen such that the electric field is constant or can be easily calculated over the entire surface. Generally, the surface should have symmetrical boundaries and enclose the charge distribution.

4. Can a Gaussian surface be any shape?

No, a Gaussian surface should be chosen to simplify the calculations and should have symmetrical boundaries. It is typically chosen to be a sphere, cylinder, or cube, but can also be other symmetrical shapes such as a plane or cone.

5. Why is a Gaussian surface used in Gauss's Law?

A Gaussian surface is used in Gauss's Law because it allows for the simplification of the calculation of the electric field. By choosing a symmetrical shape, the electric field can be easily calculated over the entire surface, making the application of the law more straightforward.

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