A current-assisted magnetic recording write head has an electrically conductive layer in the write gap between the write pole and the trailing shield. Electrical circuitry directs current from the write pole, through the conductive layer, to the trailing shield. The current through the conductive layer generates an Ampere field substantially orthogonal to the magnetization in the write pole to assist magnetization switching of the write pole. The write head's magnetic throat height (THm) is substantially the thickness of the trailing shield at the write gap, while the write head's electrical throat height (THe) is substantially the height of the conductive layer in the write gap. In embodiments of this invention, the signal-to-noise ratio (SNR) of the readback signal and the soft error rate (SER) of the recorded data can be improved with a write gap structure wherein THe is greater than THm.