Flux is the amount of a vector field that "flows" through a surface. We now discuss the electric flux through a surface (a quantity needed in Gauss's law): , where is the flux through a surface with differential area element , and is the electric field in which the surface lies. There are several important points to consider in this expression:
It is an integral over a surface, involving the electric field at the surface.
is a vector with magnitude equal to the area of an infinitesmal surface element and pointing in a direction normal (and usually outward) to the infinitesmal surface element.
The scalar (dot) product implies that only the component of normal to the surface contributes to the integral. That is, , where is the angle between and .
When you compute flux, try to pick a surface that is either parallel or perpendicular to , so that the dot product is easy to compute.
Two hemispherical surfaces, 1 and 2, of respective radii and , are centered at a point charge and are facing each other so that their edges define an annular ring (surface 3), as shown. The field at position due to the point charge is:
where is a constant proportional to the charge, , and is the unit vector in the radial direction
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