College Physics: Gauss’s Law Exercise, PHYS 212

Gauss’s law states that the net flux (a flux into a spherical surface positive, out of the surface positive) through an arbitrary closed surface is equal to net electric charge contained within the surface divided by ε_o, permittivity constant. Below is a pictorial representation of two charges contained within some surfaces. These surfaces are represented by their two dimensional projections onto the plane (paper), therefore, they appear like closed lines.

Φ₁=Flux through S₁ is (-5Q)/ ε_o= -5Q/ ε_o

Φ₂=Flux through S₂ is (-5Q+7Q)/ ε_o=2Q/ ε_o

Do the following exercise. Find the fluxes through the surfaces provided due to charges shown.