An electrophile by definition is an electron loving species.
Carbon 2 has a full octect, 2 single bonds and 1 double bond.
A nucleophile can attack the carbon and force the pi bond of the double bond to break off leaving the oxygen with a negative charge.
The carbon would then be able to form a new octet with the nucleophile that attacked it.
In essence, the nucleophile 'donated' a pair of electrons to the electrophile, carbon.
This is what we call, nucleophilic attack.
What makes carbon 2 a better electrophile than carbon 4?
Remember that single bonds are sigma bonds; double bonds are sigma + 1 pi bond; triple bonds are 1 sigma + 2 pi.
What is the significance of that? Well, pi bonds are a lot weaker than sigma bonds.
Carbon 4 has 4 bonds, which are all sigma bonds while carbon 2 has 3 sigmas and 1 pi.
The pi bond will more readily break off than a sigma bond any day.
The only way carbon 4 will undergo attack by a nucleophile is via substitution.
Notice that in carbon 4, the leaving group (Br) is on a primary carbon.
This is indication that SN2 is more likely to proceed.
In which case you'd need a polar aprotic solvent AND a very strong nucleophile to even initiate the reaction.
Basically, there are a lot more requirements to get the mojo going at carbon 4 than it is at carbon 2. I hope this helps somewhat lol. If my logic is flawed anywhere, please feel free to correct me!
EDIT: Oh yes to answer your question about 'finding the carbon with the highest partial positive charge'
Notice that when a nucleophile is attacking carbon 2, the pi bond COMPLETELY breaks off, therefore giving carbon 2 a FULL positive charge briefly.
If you remember the reaction mechanism for SN2, it forms a transitional state with 5 bonds... Also having electron withdrawing groups on the carbon will only give it a 'partial' positive charge to begin with. Why have partial when you can have full
🙂
Also, you are incorrect in thinking that carbon 4 has the most electronegative groups attached to it.
Carbon 2 has 1 double bond to oxygen so this actually counts as TWO bonds to oxygen.
Carbon 4 has 1 bond to oxygen and 1 bond to Br.
If you take a quick look t your periodic table you should quickly notice that oxygen is more electronegative that Br. This makes carbon 2 more "positive".
I think that's about it now. If you are having problems conceptually might I recommend CHAD's if you haven't done so? A lot of people rave about his videos in their break downs.
Personally I've decided to try a different source!