How does a “screwdriver” mobile antenna adjust its feed point impedance?

A "screwdriver" antenna is a popular type of HF mobile antenna that uses a small DC motor to move a contact up and down a large coil located near the base of the antenna. This motorized action physically changes the amount of wire in the active circuit, thereby varying the base loading inductance to tune the antenna to the desired frequency. Because mobile HF antennas are physically much shorter than a resonant quarter wavelength, they exhibit high capacitive reactance. They require this added base or center inductance to cancel out the capacitance and achieve a matched feed point impedance. While extending the whip or deploying a capacitance hat are valid ways to affect antenna tuning, the defining mechanism of a screwdriver antenna is its motorized adjustable loading coil.