Gauss's law for electromagnetism says surface∫E x dA = qenclosed/∈0 . If the electric field is given to be E = Ar (where r is a vector), what is the surface integral of E over the whole closed surface of the cube that spans the region from the origin to (x, y, z) = (a, a, a)?
(a) What is the charge enclosed in the cube?
(b) Compute the volume integral, ∫Δ x Ed3r inside the same cube, where the delta is equal to the DEL operator.