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Qmechanic
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What's the net flux from sphere?

I have a sphere of radius "r" , the sphere has a total charge "q" distributed equally around the surface. A point "P" is at a distance "R" from the centre of the sphere.

I have a sphere of radius $r$ , the sphere has a total charge $q$ distributed equally around the surface. A point "P" is at a distance $R$ from the centre of the sphere. As per the book, to find the net flux from the gaussian sphere with radius $R$, we use ∅ = E × ds × cos (theta) , here , we are assuming the electric field at every particular point in the gaussian surface to be "E" as constant. And thus ,it can be easily calculated as net ∅ = E × 4πr²(the area vector makes 0° with E). But , in the picture , I can see the Electric field can be seen as the total electric field by the all the points on the surface made by a solid angle infront of the point , and only one field is normal to the area vector while the others make different angles. So why do we compute it with taking E as constant. And if I'm correct, how can I find the net flux of that particular point and ultimately for the whole gaussian surface?

Aryan
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