Wireless Power trasfer
This video will answer all your questions and includes demonstrations you can replicate: 

About Wireless Power Transfer

The short version is that you need quite a lot of energy to get a reasonable result since there are lots of things that cause loss. So using magnetic fields is quite inefficient. There is, however, another attempt at wireless power that uses ultrasound instead of a magnetic field. Ultrasound is a pressure wave instead of an electromagnetic wave and may be more efficient. There's a company called uBeam that is trying to commercialize that technology, however they're still in stealth mode. There are some papers on Google scholar that discuss ultrasonic energy transfer though.