[UPSC CSE 1991] Electrostatics and Magnetostatics (Q269, 20M)

In certain region of space in vacuo, the components of the magnetic induction are (in weber per square meter) B_x = A e^{-ay} + bx B_y = A c^{-ax} + cy B_z = 0 where x, y, z, are in metres and A, a, b and c are constants. Find the relation, if any between these constants and also the current distribution that gives rise to this field. (No electric field is present). Is the current distribution consistent with the charge conservation principle?