We describe a technique for mapping the spatial variation of static electric, static magnetic, and rf magnetic fields using a pulsed atomic or molecular beam. The method is demonstrated using a beam designed to measure the electric dipole moment of the electron. We present maps of the interaction region, showing sensitivity to (i) electric field variation of 1.5 V/cm at 3.3 kV/cm with a spatial resolution of 15 mm; (ii) magnetic field variation of 5 nT with 25 mm resolution; (iii) radio-frequency magnetic field amplitude with 15 mm resolution. This new diagnostic technique is very powerful in the context of high-precision atomic and molecular physics experiments, where pulsed beams have not hitherto found widespread application. Comment: 6 pages, 12 figures. Figures heavily compressed to comply with arxiv's antediluvian file-size policy