In this work the junction condition formalism is used to build up wormholes
from two identical spacetimes, which are exact solutions of the Einstein-M
axwell equations. The surgery produces a class of wormholes in which the am
ount of exotic matter is controlled by an external magnetic field. It is de
monstrated that the total amount of exotic material is a decreasing functio
n of the magnetic held intensity and that most of the remaining material is
concentrated near the poles of the junction. A region in which there is no
violation of the null and strong energy conditions is determined. The rang
e of applicability of the model is discussed in some detail.