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glennpagano
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I have been studying Gauss' law and almost all of the problems I have been doing just have me integrate dA alone into A. I was wondering when do you actually have to do some more in depth integration.
glennpagano said:What if it is not perpendicular? Then you will have E[tex]\oint cos \phi dA[/tex]. Then you can just pull out the cosine then because it is constant when compared to dA.
If the E is not constant then will you still have to integrate it? Do you have to make it with respect to dA first? The more info the better. Right now, for most occasions I see Gauss' law as EA=q/epsilon naught.
Gauss' law is a fundamental law in physics that describes the relationship between the electric flux through a closed surface and the electric charge enclosed by that surface.
Gauss' law involves the calculation of the electric flux, which is represented by the integral of the dot product between the electric field and the surface area element (dA). The surface area (A) is used to determine the direction and magnitude of the electric field at a point.
Different situations may arise where dA cannot be integrated into A for Gauss' law. This includes situations where the electric field is not constant or if the surface is not a perfect shape, such as a sphere or cylinder.
When dA cannot be integrated into A, the calculation of electric flux becomes more complicated. In these cases, the integral must be evaluated over the entire surface, rather than a simplified closed surface. This often involves breaking the surface into smaller, more manageable pieces.
Yes, there are other factors that can affect the integration of dA into A for Gauss' law. These can include the presence of other charges outside of the closed surface, or if the surface is not perfectly symmetrical, making it difficult to determine the direction of the electric field at every point.