Electromagnetic charging
What you describe is theoretically possible, but very inefficient, and probably not feasible. Proof:

\$3V\$ at \$2mA\$ is \$6mW\$. This is how much power you need to receive to make your thing work. The question is this: how much do you have to transmit?

If you have a \$1W\$ transmitter attached to an isotropic radiator (such things don't exist, but we will address that later), then for any sphere centered on that radiator, there is \$1W\$ of power. But, this power is spread out over a sphere of increasing area as we get farther away. This is the inverse square law. Knowing this, we can calculate the field strength from your \$1W\$ isotropic radiator at some distance \$r\$, by taking that \$1W\$ of power and dividing it by the surface area of a sphere. At \$20km\$, the field strength from your \$1W\$ isotropic radiator is:

$$ \frac{1W}{4 \pi (20km)^2} \approx 199pW/m^2 $$

Let's just say on your device you have made an antenna that can collect all the RF energy passing through a square meter. You will then receive 199pW, which isn't anywhere near the \$6mW\$ you need. In fact, you need about thirty thousand times more (\$6mW / 199pW \approx 30151\$). You could invest in a \$30kW\$ transmitter, but that's probably not what you had in mind.

You can make this system more efficient by sending less energy into space where your receiving device isn't. That is, you can use a directional antenna. We need an antenna that is 30151 times stronger than an isotropic radiator in the direction of the receiving device. That is, we need a gain of \$ 10 log(30151) \approx 45dBi \$. (more about dBi) You could get about that from a very directional antenna, like one with a large parabolic reflector.

So, if you can have a big, directional antenna, you can aim it at your device (hard, because the antenna is so directional), and your receiver can collect all the energy in a \$1m^2\$ area (probably not possible, if you want it to be small), you could power your device with a \$1W\$ transmitter. You are still not very efficient:

$$ 6mW / 1W = 0.6 \text{% efficient} $$

and all of those assumptions are pretty generous. By the time you take into account other inefficiencies in the system, the practicalities of making these devices small, aiming the antenna, etc, RF power transmission doesn't sound so great.

How about a solar panel? The sun is also an isotropic radiator of electromagnetic energy, and it's far away, and suffers from the same inefficiencies. But, it's free, and transmits at a power of about \$383YW\$, (solar luminosity) with the field strength being as much as \$1kW/m^2\$ at Earth's surface (Earth's insolation).