In a region of space there exists the following electric field (in spherical coordinates) : E~ (r, θ, φ) = (3r 2 cos(θ)ˆr − r 2 sin(θ) θˆ) N m2C Find the amount of charge contained in the region of spaces described by the upper (z ≥ 0) hemisphere of a sphere radius 50cm centered at the origin. Do this two ways, making use of: a) The integral form of Gauss’s law b) The differential form of Gauss’s law