Actually, this is a common thing to wonder.
There is a dual to this. When you have devices sharing a common winding and magnetic flux(Magnetic "current") it makes a perfect dual for devices sharing a common electric conductor. Nice picture from wikipedia:
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You can also take a look at "Magnetic Circuits". You can start learning some fun terms when you go into these concepts in detail, like "Magnetic Capacitance," it seems that my flux does have capacitance.
The way you can determine how much energy passes through a transformer can be broken down into a magnetic circuit that works just like an electric circuit with different units. Magnetic Circuits are an analog of Electric Circuits, which are much easier to work with for many many reasons.
Think of it like a voltage source or a current source. They are direct analogs, but when you build a voltage source it is a hell of a lot easier than a current source.
Side Note
The magnetic flux is shared in a core due to the fact that magnetic flux is perpendicular to the wire, the issue with electric flux is that it points between two surfaces, not looped around. If it looped around a dielectric would get the job done.
In relation to the capacitor inside the other
IF the smaller becomes bigger, it will end up acting like two coupling capacitors with a series resistor between them, as it gets smaller, the overall electric field will be minimal, but you could put a big big E-Field in there, not nearly as effective as a transformer.
Four days ago, I received a news email from a technology site I follow. One of the news was that Microsoft registered a patent to do what you're asking.
Here is the link for the patent.
The news site is "Clube do Hardware" and the news about this theme was in "Boletim 1440". You can see the (old) news bulletin in this page. Although this specific edition is not yet on the page, it may appear there soon. (Sorry, due to the copyright terms, I can't post the news here)
Best Answer
Essentially none. The magnetic field isn't strong enough to disrupt the electric field used for sensing.
However, many phones contain a magnetometer for measuring compass direction, which definitely will be affected by a magnet. I've seen claims of magnetic case clasps permanently affecting the calibration of the magnetometer, but I don't know how true these are