In a region of space where there are no conduction or displacement currents, it is impossible to have a uniform magnetic field that abruptly drops to zero. To prove this statement, use the method of contradiction: Assume that such a case is possible, and then show that your assumption contradicts a law of nature.
(a) In the bottom half of a piece of paper draws evenly spaced, horizontal lines representing a uniform magnetic field to your right. Use dashed lines to draw a rectangle abcda with horizontal side ab in the magnetic field region and horizontal side cd in the top half of your paper where B = 0.
(b) Show that integration around your rectangle contradicts Ampere's law.