The electric flux through a surface is proportional to the number of field lines crossing that surface. The electric flux is obtained by evaluating the surface integral Φ = ∮ S E → · n ^ d A = ∮ S E → · d A → , Φ = ∮ S E → · n ^ d A = ∮ S E → · d A → , where the notation used here is for a closed surface S

Gauss’s law relates the electric flux through a closed surface to the net charge within that surface, Φ = ∮ S E → · n ^ d A = q enc ε 0 , Φ = ∮ S E → · n ^ d A = q enc ε 0 , where q enc is the total charge inside the… For spherical symmetry, the Gaussian surface is also a sphere, and Gauss’s law simplifies to 4 π r 2 E = q enc ε 0

electric flux — dot product of the electric field and the area through which it is passing. spherical symmetry — system only varies with the distance from the origin, not in direction. magnitude — proportional to the portion of the field perpendicular to the area. electric flux through a surface — proportional to the number of field lines crossing that surface.