Electromagnetism - Gauss' Law

If an electric field is given in a certain region by E_x = 0, E_y = 0, E_z = kz, where k is a nonzero constant, which of the following is true? 

A. There is a time-varying magnetic field.
B. There is charge density in the region.
C. The electric field cannot be constant in time.
D. The electric field is impossible under any circumstances.
E. None of the above.

(GR9277 #64)

Solution:

Gauss’ Law: ∇ ∙ E = ρ/ε₀

For E_x = 0, E_y = 0, E_z = kz

∇ ∙ E = ∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z = 0 + 0 + k = k

Since ∇ ∙ E ≠ 0 → There is charge density in the region.

Answer: B