If you were wearing the sweater shown and rubbed your hand on it, you too would gain some negative charge on your hand. Then when you directly touch a metal conductor, like a door knob, you will feel a shock. This is called Conduction. From this scenario, where does the negative charge go when you touch a door knob?
When you rub your hand on a sweater and then touch a metal doorknob, the process involving the transfer of charge is known as electrostatic discharge (not conduction in the strictest sense, as conduction refers to the movement of charge within a material). The scenario you're describing is a classic example of triboelectric charging followed by an electrostatic discharge.
Here's what happens step-by-step:
1. Triboelectric Charging: When you rub your hand on the sweater, you're generating static electricity through the triboelectric effect. The materials of your hand and the sweater are likely made of substances with different tendencies to gain or lose electrons. Due to this, electrons are transferred from one material to the other. If the sweater tends to give up electrons, your hand will gain some negative charge from the sweater by attracting its electrons.
2. Charging Your Hand: When these extra electrons accumulate on your hand, it becomes negatively charged.
3. Electrostatic Discharge: Once you touch the metal doorknob, which is a good electrical conductor, the excess electrons on your hand are rapidly transferred to the doorknob. This happens because the metal's free electrons can move easily throughout the material, allowing it to quickly equalize its electric potential with that of your charged hand. The excess negative charge you've accumulated is neutralized by moving to the larger, grounded, conductive object.
The 'shock' you feel is the sudden movement of electrons from your hand to the doorknob. These electrons are seeking the lowest potential energy state, which is typically "ground" or a place where the excess charge can be dispersed. If the doorknob is connected to the ground (earth) through the building's electrical system or structure, the electrons then continue to move until they are evenly distributed, thereby neutralizing the negative charge. If the doorknob is not grounded, it will simply become negatively charged until it reaches an equilibrium with the charge of your hand.
In essence, the negative charge goes from your hand into the doorknob and then into the ground (if the doorknob is grounded), where it's distributed over a vast area, essentially becoming negligible.