I have calculated the energy and the wave function of an electron trapped near the intersection of two quantum wires. I have also shown that when the trapped electron is subjected to a magnetic field, the energy of the electron increases while the size of the wave function shrinks. It can be demonstrated theoretically that the introduction of the magnetic field can lead to the release of the electron from the trapped to the freely propagating state. The effect has the potential for use as a switch or as a magnetic field sensor. (C) 2004 American Vacuum Society.