Solution to 1986 Problem 79

(A) Assume the upward direction is y and the horizontal direction is x. Then B_y = 0 everywhere and B_x does not change as you go in the x direction (B_x does, however, change as you go in the y direction). Thus,
\begin{align*}\frac{\partial B_x}{\partial x} + \frac{\partial B_y}{\partial y} = 0\end{align*}
So, the equation is obeyed.
(B) shows a constant magnetic field, which is clearly divergenceless.
(C) shows the magnetic field due to a current loop, which is clearly possible.
(D) shows the electric field due to a point charge (i.e. an electric monopole); since magnetic monopole's do not exist (which is equivalent to the state \nabla \cdot \mathbf{B} = 0), this field configuration is not possible. Thus, answer (D) is correct.
(E) is the magnetic field around a wire, which is clearly possible.

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