power supply - How can i transfer 12 V, 50 Hz, 1 A wirelessly?

I want to transfer electical power wirelessly from a transmitter to a receiver coil.

Input energy is provided by a single phase step-down transformer - 230V/12V AC, 50 Hz, 1,000 mA.

Using the 12 V AC output I want to transfer as much of the available power wirelessly from transmitter coil to the receiver coil over a distance of 5mm. How can that be done ?
What calculations should i solve so as to achieve this ?

I want to transmit across 5 millimeters.
The radii of the transmitter and receiver coils I am currently using are are 5cm and 2cm respectively

After transmitting it to the receiver coil, I wish to rectify and filter it and then regulate it to 5V DC use it to charge a battery.

I want 5V DC at the end of the circuit, but how can I accomplish that ?

What calculations and equipment specifications do I have to use so that I can figure this out?