How does the distance between the transmitting antenna and the receiving antenna…

How does the distance between the transmitting antenna and the receiving antenna affect the amount of current flowing between the two systems?

Actually, there is no current flowing between the two systems. Current flowing up and down the transmitting antenna causes current to flow up and down the receiving antenna, but there is no direct connection between the two and they do not share any current. That explains how an isolated radio can still receive music. But the amount of current flowing in the receiving antenna does depend on its distance from the transmitting antenna. When the two are very close, the charge in the receiving antenna responds directly to the charge moving on the transmitting antenna. As they move apart, this direct response quickly dwindles to virtually nothing. In its place, a new effect appears. The transmitting antenna creates radio waves that exist apart from the accelerating charges that created them. The strength of the radio wave diminishes in power roughly as the square of the distance from the transmitting antenna. The electric and magnetic fields diminish in power roughly in proportion to this distance. The current flowing in the receiving antenna also falls roughly in proportion to this distance.

How does turning the dial on your radio allow your radio to distinguish between …

How does turning the dial on your radio allow your radio to distinguish between stations? How does the receiver only recognize one frequency at a time?

When you turn the dial on your radio, you are adjusting the resonant frequency of its tank circuit (or some electronic equivalent). The tank circuit only responds to charge sloshing on the antenna when that charge is moving back and forth at the tank circuit’s resonant frequency. When you tune the tank so that its resonant frequency is the same as the broadcast frequency of your favorite radio station, it only responds to charge moving up and down at that frequency. As a result, your radio detects signals from your favorite station but no others.

How good are store bought antennas and if they are better than factory issue, wh…

How good are store bought antennas and if they are better than factory issue, which ones are most advantageous?

Ultimately the only things that matter about an antenna are (1) how much charge it moves in response to the correct radio transmission and (2) how little charge it moves in response to the wrong radio transmissions. Most store bought antennas probably just boost the amount of moving charge by attaching an amplifier to an otherwise undistinguished antenna. While that trick will increase the amount of charge moving in response to the correct transmission, it will also increase the amount moving due to undesired transmissions. Almost everything electrical transmits radio waves and these may well interfere with your reception. For example, your neighbor’s lawn mower may send out radio waves and introduce noise into your music. Just amplifying the antenna signal does nothing to eliminate that problem. Your best bet is to find a directional antenna; an antenna that responds most strongly to radio waves coming from a particular direction. TV antennas are typically directional, with many separate antenna elements. Satellite dishes are highly directional.