smallest possible length of copper wire, where I can measure capacitance via multimeter
You can't easily measure capacitance with a multimeter unless it has a capacitance meter built in.
Capacitance in parallel wires will be tiny because A (area) is so small and d (distance) is too great. This will make it very difficult to show.
You won't be able to make any dynamic readings with a digital meter. The numbers will jump around for a fraction of a second but you will not be any wiser afterwards. With an analog (moving coil) meter you may see the needle flick in proportion to the current or voltage.


As MarkU has suggested, two large sheets of aluminium foil separated by a layer of cling-film / food wrap may be more helpful. I've never tried this but here are some experiments that come to mind.


Measure the are of the alu-foil plate. Place it on the table.
Cover with cling film. If you can measure the film thickness and look up the dielectric constant for PVC you may be able to calculate the capacitance value.
Apply the second layer of foil and press the whole sandwich together by weighing down with books.
Somehow, make an electrical connection to each plate.
Charge up the plates using a battery or power supply.
Connect a multimeter set to volts and measure the voltage across the plates.
Disconnect the power supply and watch the voltage drop as the capacitor discharges through the multimeter. Try and estimate how long it takes to discharge by 63%. This is the RC time constant where R is the input resistance of your multimeter and C is your home-made capacitor. Typically digital meters have a 10 MΩ.


If all that works you can repeat the experiment with additional layers of food-wrap between the foil. This should reduce the capacitor value as the 'd' term is increasing.

Has anyone else tried this? Any other ideas?

Let us know how you get on.