A power system has a wireless power transmitting device and a wireless power receiving device. Coils in the power transmitting and receiving devices are used to transmit and receive wireless power signals. The coils may include pot core coils, figure eight coils, solenoids, and other coils. A solenoid array may extend under a charging surface in a wireless power transmitting device. Solenoids in the array may be separated from each other by small gaps. Solenoids may have rectangular outlines, hexagonal outlines, or other shapes. Pot core coils may have a magnetic material with a circular groove of a groove of other suitable shapes that contains wire windings. Figure eight coils may have first and second adjacent magnetic cores with respective counterclockwise and clockwise wire windings. Magnets and other alignment structures can be used to help align coils in transmitting and receiving devices.