The energizing coil was a component used in the transporter system.
When a Romulan interphase generator interfered with the beaming of Geordi La Forge and Ro Laren in 2368, transporter chief Brossmer requested more power to the primary energizing coil from Engineering. (TNG: "The Next Phase")
In 2372, while the beaming of four crewmembers was already underway, the energy of an exploding runabout travelled along the transporter beam and blew up Deep Space 9's primary energizing coils, which prevented rematerialization and stored the patterns in the pattern buffer. (DS9: "Our Man Bashir")
In 2373, a remat detonator interfered with a transporter's integration matrix during transport. Jadzia Dax and Worf attempted to transfer the endangered transporter pattern to the secondary pattern buffer and boost the gain on the energizing coils, but it could not be boosted enough to save Trentin Fala. (DS9: "The Darkness and the Light")