However, existing solutions are limited to near contact distances and do not provide the geometric freedom to enable automatic and un-aided charging. We introduce quasistatic cavity resonance (QSCR), which can enable purpose-built structures, such as cabinets, rooms, and warehouses, to generate quasistatic magnetic fields that safely deliver kilowatts of power to mobile receivers contained nearly anywhere within. A theoretical model of a quasistatic cavity resonator is derived, and field distributions along with power transfer efficiency are validated against measured results. An experimental demonstration shows that a 54 m3 QSCR room can deliver power to small coil receivers in nearly any position with 40% to 95% efficiency. Finally, a detailed safety analysis shows that up to 1900 watts can be transmitted to a coil receiver enabling safe and ubiquitous wireless power.