Linac4 is the first element of the LHC Injectors Upgrade Project. It is a normal conducting linear accelerator for H--ions and will replace the old Linac2 as linear injector of protons for the CERN accelerators. A new transfer line will link Linac4 to the Proton Synchrotron Booster (PSB).
This presentation contains an overview of the new Linac4 electromagnets, but concentrates on the design of the Linac4 Transfer Line Quadrupole Magnet. We present the different steps of optimization of the magnet yoke. At the same time, we discuss how the final magnet design is not only a product of the requirements of the magnetic field but also of its interfaces with other accelerator technologies. In particular, the power converters and the alignment strategy proved to be important elements in determining the final Transfer Line layout and therefore the final Quadrupole Magnet design.