Electricity in your finger moves in response to the electricity in the phone. The electricity in the phone moves in response to the electricity in your finger moving in response to the electricity in the phone.
Whether this counts as “electricity moving between the two” is really just semantics. This is just a basic capacitor, and while some people may say that “electricity flows through the capacitor” no electrons are crossing that gap. The influence of the involved electrons, however, does cross the gap.
The charge comes from the screen. The screens are layered with an electrically conductive transparent material called iron tin oxide. When your finger (or any conductor) touches the screen, a very small amount of charge gets moved to your finger, and this causes a voltage drop at that part of the screen. This small, localized voltage drop is how the screen knows what part of the screen you touch. There are a couple different ways that different screens detect where the voltage drop is. But that’s the gist of it.
Electricity doesn’t enter your finger, but rather your finger has its own charges. Your finger acts as what’s called a dielectric. Basically, it interferes with the electric field across the capacitor, changing the capacitance, which means the capacitor can hold more charge, so some current flows. That flow of current is what the screen interprets as touch.
C=Q/V
C=εA/d
C is capacitance, Q is charge, V is voltage
ε is the electrical permittivity of the dielectric, ε_0 specifically is the permittivity of free space and a dielectric will increase that.
A is the area of the two plate of the capacitors (which doesn’t change) and d is the distance between those plates (which also doesn’t change
Since we only change ε, C changes. The voltage of the circuit doesn’t change, so since C changed, the charge must change. For charge to change, it requires a current (I = dQ/dt)
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