Cant understand Gaussian surface

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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
robphy
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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|
 

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