Cant understand Gaussian surface

In summary, gaussian surfaces are hypothetical closed surfaces used in conjunction with Gauss' Law to relate electric flux and charge enclosed. They are chosen based on the symmetry of the problem to simplify calculations and solve for the electric field.
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mujadeo
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Homework Statement


Can someone please explain what use gaussian surfaces have, in really simple terms?
I don't really understnd the point of wrapping an imaginary surface around a charge, when we can just do the calcs without the imaginary surface.
Also if there are preset gaussian surfaces that are commonly used (sphere, cube, cylinder) how do we know which surface to use? and also wouldn't perfect shapes (gaussian) be intrincially and largely inaccurate, and if so, then again what is the point of superimposing an imaginary surface over the real thing?


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  • #2
A gaussian surface is a hypothetical [closed-]surface that encloses some volume of interest.

When used with Gauss' Law [one of the Maxwell Equations], it relates the outward electric-flux through that surface with the total charge enclosed within that surface. This relationship is independent of the choice of gaussian surface so long as the same charges are enclosed.

If the surface is [chosen] sufficiently "nice" so that the total electrix-flux [tex]\oint \vec E\cdot d\vec A[/tex] can be expressed more simply, one may be able to go further and solve explicitly for the electric-field everywhere on that gaussian surface. That's why problems with spherical [respectively, cylindrical] symmetry suggest using a spherical [respectively, cylindrical] gaussian surface. Some problems are more easily solved by exploiting the symmetries of the problem with Gauss' Law.
 
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basically we use a gaussian surface to make it easier to solve for E. For example integral(E.da) = |E|*(surface area of gaussian surfce) then we relate this to the total charge enclosed or the density at points within a volume. The symmetry of the surface chosen allows us to say E=|E|
 

1. What is a Gaussian surface?

A Gaussian surface is a hypothetical surface used in Gauss's law to simplify calculations of electric fields. It is a closed surface that encloses a charge or a group of charges.

2. Why is a Gaussian surface used in Gauss's law?

A Gaussian surface allows us to apply Gauss's law, which states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of the surrounding medium. This simplifies calculations and makes it easier to determine the electric field in a given region.

3. How is a Gaussian surface chosen?

A Gaussian surface is chosen based on the symmetry of the electric field and the distribution of charges. It is typically chosen to be a closed surface that is perpendicular to the direction of the electric field, making the calculation of the electric flux simpler.

4. Can a Gaussian surface be any shape?

No, a Gaussian surface must be a closed surface to apply Gauss's law. It can be any shape as long as it encloses the charge or charges of interest. However, choosing a surface with high symmetry can make the calculations easier.

5. How does a Gaussian surface relate to electric fields?

A Gaussian surface is used to calculate the electric field at a point near a charge or a group of charges. It allows us to apply Gauss's law, which relates the electric field to the charge enclosed by the surface. The electric field at a point is perpendicular to the Gaussian surface and its magnitude is inversely proportional to the distance from the charge enclosed.

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