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Gauss's law for electromagnetism says _surface∫E x dA = q_enclosed/∈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.

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