A read/write head for a disk drive having a magnetoresistive (MR) read element and an inductive write element suitable for perpendicular recording of data onto a disk having a media layer in which the data is stored perpendicularly to the planar surface of the disk and a soft underlayer (SUL) underneath the media layer to provide a low reluctance return path for the magnetic recording field. The write element includes a vertically-oriented write pole and a downstream write shield that is magnetically connected to the write pole by a magnetic via. One or more pancake coils are employed to produce a magnetic field that is focused by the tip of the write pole which is relatively smaller than the remainder of the write pole. The design of the write shield, the write pole, the magnetic vias, and the conductive coils is such as to provide an optimal magnetic field gradient and an optimal write field strength.