± Calculating Flux for Hemispheres of Different Radii Learning Goal:

To understand the definition of electric flux, and how to calculate it. 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): ΦE=∫E⃗ ⋅dA⃗ , where ΦE is the flux through a surface with differential area element dA⃗ , and E⃗ 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. dA⃗ 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 E⃗ ⋅dA⃗ implies that only the component of E⃗ normal to the surface contributes to the integral. That is, E⃗ ⋅dA⃗ =|E⃗ ||dA⃗ |cos(θ), where θ is the angle be