How to Apply Gauss's Law for Symmetrical Electric Objects?

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To apply Gauss's Law for symmetrical electric objects like an infinite cylindrical shell, it is essential to choose an appropriate Gaussian surface that aligns with the symmetry of the problem. For cylindrical shells, the Gaussian surface should be coaxial with the cylinder, allowing for the electric field to be uniform across the surface. The contribution to the integral of E·A comes only from the faces of the Gaussian surface that are perpendicular to the electric field, as parallel faces do not contribute. Understanding the symmetry helps simplify calculations, as the electric field magnitude remains constant across these perpendicular surfaces. Mastering these concepts will aid in resolving electrostatic problems effectively.
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Homework Statement



I need a strategy to resolve electrostatic problems such as the infinite cylindrical shell of radius r1 and r2 of non conducting material. I'm confused in applying a gaussian surface in this and others cases. Is there a recipe for it?

Homework Equations



Gauss's law.


The Attempt at a Solution

 
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Usually, the faces of a Gaussian surface are either perpendicular or parallel to the electric field. The faces that are parallel contribute nothing to the sum (or integral) of E·A (or E·dA). Also, the field is usually of equal magnitude over the faces where it is perpendicular, so those have a contribution of simply E·A.
 

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