To realize charging while in non-contact processing operation for the purpose other than charging. An approach of a portable electronic device 2 with a rapid bulk electricity storing module 20, which is a chargeable power source, is detected at the side of a power transmitting device 1, and power transmission for charging the rapid bulk electricity storing module 20 is executed in response to thedetection of the approach. A power source can be charged in operation for non-contact authentication which is executed when a device approaches an authentication device.