I was wondering how Ethernet equipment (for example a switch) knows that something have been plugged in and is up ?
Is there a pair of copper wire dedicated for that ? Or a bit exchange ? On which wire ?
It's called Autonegotiation: Wikipedia
Ports looking for a link send "link pulses" on the data lines that (mostly) convey speed(s) and half/full duplex capabilities. When both sides agree on common link parameters, the link comes up. Some Ethernet variants need to negotiate additional parameters, e.g. 1000BASE-T negotiates the clock master/slave and data pair matching. For precise details, check IEEE 802.3 Clauses 28, 37, and 73.
In the absence of autonegotiation - when it is deactivated on a port and a certain speed and duplex mode is manually set - the other side is (usually) able to sense the port speed by line behavior/encoding. However, the duplex mode cannot be sensed and is a common source of problems with autonegotiation disabled.
Basically, for "knowing that something have been plugged in", there is a specific mechanism on the physical layer called "link pulse"
These link pulses are (now) included in the whole "autonegociation" mechanism but were existing prior (this is why your 10Mb hub was able to sensing something plugged in)
There is a really good Wikipedia article on this https://en.wikipedia.org/wiki/Autonegotiation#Electrical_signals