Why isn't my Hand repelled by a Current-carrying wire? I was watching this interview with Richard Feynman on Youtube, (Watch it from 3:55 onward): https://www.youtube.com/watch?v=MO0r930Sn_8
Now he mentions that the reason why one's hand doesn't go through the arm of a chair (or anything 'solid' for that matter) is due to electrical forces of repulsion.
So what I comprehend from that example (correct me wherever I'm wrong), is that two separate bodies can't technically 'touch', at least not at the atomic level, and their inability to come in 'contact' (very strictly speaking) is due to the electrical repulsion that is produced between them. 
Now this seems like an excellent explanation (well, it did come from Feynman here), but it wasn't long before I had began having doubts....
I don't think this really counts as an 'experiment', but earlier this week I was handling an insulated copper wire maintained at about 120 V (Don't ask me what I was trying to do then....hint: Electrolysis) which has a plastic jacket that's barely 0.5 mm thick. Since there was current flowing through the wire (and a fairly good amount of it too, I guess..), from Feynman's explanation, I'd expect my hand to be repelled by the wire, even a teeny tiny, just discernible force of repulsion, would've been sufficient to convince me of Feynman's explanation, but obviously ('obvious' from common experience)  that did not happen.
It wasn't that I was actually expecting the wire to repel my hand, but doesn't this count as proof against Feynman's statement?
So did Feynman give us an oversimplified explanation, or is there something I didn't take into account in my "experiment" ?
Edit: Also, would I actually experience a force of repulsion (by 'experience' I mean actually 'feel' the repulsion as I grab hold of it) if I were to grab a small sphere that has a net charge of (say) a milli-coloumb ?
 A: Feynman was talking about electrostatic repulsion, you were holding a current carrying wire, they are different situations.
Even if you had a non-current carrying wire in your hand,  for the same reason, that is due to  electrostatic repulsion, this repulsion would have stopped the wire passing through your hand. 
The current would not make much difference in the current carrying wire, as regards repulsion in the sense that Feynman meant it.
In other words, you would still feel the electrostatic repulsion of a "dead" wire.  A relatively small number of electrons passing along it, would not  have much impact,  if any,  on  the overall electrostatic charge/repulsion,  carried by much greater total number of atoms in both the wire  and your hand.

So did Feynman give us an oversimplified explanation, or is there something I didn't take into account in my "experiment" ?

If you watch a similiar video on magnetism, you will see the lengths Feynman goes to to avoid oversimplification, because he basically tells the interviewer that math is required and he is not prepared to explain it without the math.

Also, would I actually experience a force of repulsion (by 'experience' I mean actually 'feel' the repulsion as I grab hold of it) if I were to grab a small sphere that has a net charge of (say) a milli-coloumb ?

No, how would you know the difference (as it's so small) between that and say,  a wooden ball compared to the electrostatic repulsion of your hand and the object? 
A: 
Now he mentions that the reason why one's hand doesn't go through the arm of a chair (or anything 'solid' for that matter) is due to electrical forces of repulsion.

Your arm and the chair and usually anything we come into contact with is electrically neutral, i.e. there are as many positive charge as there are negative in the material. The repulsion occurs because the negative charges are on the "outside" of the atoms and the organized lattice of solids. They are bound in quantum mechanical states which need specific energy to extract each single electron. ( this can be very little, like rubbing the cat and then sparks can fly when the electrons fall back and neutralize the material once more) . The repulsion between two neutral objects comes because electrons repel electrons, and the outer layers are negative.
An insulation of a wire keeps the same geometry, of negative outside charges both of your hand and of the insulation. 

Since there was current flowing through the wire 

The current in the wire are electrons drifting due to the potential difference on the two ends the metal of the wire. The insulation isolates you from any effects of these electrons, fortunately, by construction.
A: 
would I actually experience a force of repulsion (by 'experience' I mean actually 'feel' the repulsion as I grab hold of it) if I were to grab a small sphere that has a net charge of (say) a milli-coloumb ?

Do the experiment.


*

*Obtain a small hollow sphere made of latex from your nearest party supply store.  We call them "balloons".  Inflate it into its spherical form.

*Obtain a cat.  Induce a charge on the sphere by rubbing it vigorously against the cat.  Keep in mind that five of the six ends of a cat are sharp enough to puncture the sphere.

*Remove the cat and place your hand close to the charged sphere.
Is the sphere repelled or attracted to your hand?  When I have tried this experiment it is attracted. Can you deduce why?
Can you charge up the balloon enough to overcome gravity?  That is, can you stick the balloon to the ceiling using only the attractive power of the static charge?  If you can do that then you can work out interesting facts about the relative strength of the static force and the gravitational force.
A: This is a general simplification of the issues.  The Standard Model of how we see the universe includes four forces, Strong, Electromagnetic, Weak and Gravitational forces.  They have relative strengths in that order.  Of those, Strong and Weak forces act only over very small ranges, while electromagnetic and gravitational forces act over infinite range though their effect drops via an inverse square of the distance.
When two macro solid objects, that is big items like you and a chair are involved, Strong and Weak forces are ignored, they are at sub atomic levels.  Gravity is also insignificant at those scales as it is so much smaller in scale than Electromagnetic, to be significant takes larger objects than you and a chair as compared to E-M, so Electromagnetic is the one we are dealing with.
Atoms are made of Nuclei which is actually seen as a cloud of Neutrons and Protons. EM forces would pull this apart, but at those ranges Strong Force comes into play and overpowers the EM repulsion and is largely responsible for holding the atom together.  The nucleus is surrounded by another cloud of electrons, which are largely held together by the EM force as they are attacked to the nucleus, but repulsed by each other so the do not actually collapse into the nucleus, instead bounce around it.  You can think of it as the old orbital drawings, but it is now considered to be more random cloud shells.
Molecules are made up of two or more atoms that are sharing electrons, that is the clouds somewhat merge with the electron sometimes being around one nucleus, sometimes another, and this holds the molecules together until something more enticing comes along.
When an atom, or a molecule comes near another, unless chemistry says, hey, I want to bond with that, the typical response is that the cloud or one object is repulsed by the other due to the EM force.  But, most of an object, even one we call a solid, is actually space between atoms and molecules, so a lot of times the objects my not actually really interact and the molecule may pass right through that solid without being repulsed.
You, and the arm chair are not molecules, you are collections of molecules.  Each individual molecule of you would experience that repulsion or maybe be too far away from any molecule of the chair to start to pass through.   But, those repulsed would also be repulsed by other molecules of your body and pushed back forward.  The odds of a given molecule penetrating far into the solid of the chair are slim, and the molecules of your body, very unlikely, though a few, here and there may actually do so.  In general though, you have a lot of molecules that make up your body and will be pushed by the many molecules of the chair, and pushed back towards the chair by EM forces from all different directions to an equilibrium.  We sense that as we are touching the chair, but in reality no real contact is made, we are somewhat floating on the chair held up by the mutual EM repulsion for the electrons making up the molecules of our body and those making up the chair.
If the chair were not solid but fluid or gas, its molecules would be further apart and less able to reach a similar equilibrium, less able to cause that floating to occur and we might well then pass through.
That is a simplification, and some not stated 100% true, but close.
This is different than the EM force felt from the current in an electrical wire.  Yes, each electron in your hand/body would be repelled, but each nucleus would be equally attracted with a net of near zero.
A: Did your hand pass through the cable? No, you can feel its weight when you hold it. It pushes down upon you, but doesn't pass through. This weight you feel is the force the wire and its insulation are exerting upon you via electrostatic repulsion.
Electricity in the traditional sense will not increase the magnitude of this force, as it comes from the electrons and protons on the surface of the object you're touching-- the insulating cable. Besides, current flow through a wire doesn't increase the number of charge carriers (i.e. electrons) anyway, so even if the cable conductor was contributing to the sense of touch, nothing would change when current flows through it.
As for your question about 'experiencing' a force from a sphere with a small net charge: humans have no net charge, and so to a good approximation, we don't feel any repulsion or attraction forces between us and charged objects. The only reason that this breaks down when we 'touch' an object is that electrons tend to be closer to the surface than protons (this is because atoms are largely empty space with huge electron clouds around them). The closer that charged particles are, the stronger the repulsion/attraction force between them. This results in a net repulsive force as we get close to an object. But I mean very close. This is called touch.
Here's a an image (Courtesy of the Wikimedia Foundation) of a hydrogen atom where you can see the ridiculously tiny atom in the center, around 100,000 times smaller than the electron cloud!

When our hand is, say, $1 \; \mathrm{cm}$ away from an object, that tiny difference in the distance to the electron cloud and the distance to the proton is insignificant. What is $1.1$ angstroms (~$10^{-8} \; \mathrm{cm}$) compared to $1 \; \mathrm{cm}$? But when we get close enough to an object, this tiny difference in distance really matters. The electron clouds of the atoms on our skin overlap with those of the object, and since like charges repel, we feel a force.
I suppose that technically, if a conductive sphere had a net negative charge, then there would be more electrons on the surface and we would experience a stronger force when touching it from the same distance. But our hand and the object will come to an equilibrium where we exert just enough pressure upon it to counteract gravity, and so feel the same force-- just with an extremely slightly greater separation between our hand and the sphere. But that effect would be so incredibly minute (i.e. the amount of charge required for anything significant would be absurd) that there's no way we would be able to perceive it without instrumentation.
A: Consider a different situation: you watched an amazing lecture on magnetic repulsion and attraction. Then you put a wood stick by the magnet and...nothing.
Why not? Well, the magnet has a strong magnetic field around it. While the wood stick, at macroscopic scale, has none.
Similarly, your wire at 120V above ground has some electric field around it (albeit a small one, we'll get to that) whereas your body probably doesn't have any net electric charge (that is, equal numbers of protons and electrons) and so at macroscopic scales, no electric field. So you won't interact with the wire in any noticeable way.
That is until you get to atomic scales, "touching" the wire's insulation. And now the electric fields of the individual protons and electrons you are made of become relevant. These fields are quite strong at subatomic scales, but at macroscopic scales they all cancel out.
Furthermore, a wire at 120V doesn't have very much net electric charge at all. It's missing a few electrons compared to its (ostensibly neutral) surroundings. The amount of electrons its missing depends on its capacitance to the surroundings. For a reasonable estimation of what your setup might have been, with some wires separated by at least some cm, that capacitance is going to be on the order of femtofarads.
Capacitance is defined as charge divided by voltage, like so:
$$ C = {q \over V} $$
So let's say there's a 10fF of capacitance between your two wires. With a bit of algebra:
$$ 1\cdot10^{-14}\:\mathrm{fF} = {q\over 120\:\mathrm V }\\
8.3 \cdot 10^{-17} \:\mathrm C = q
$$
Here the C is a unit of charge: coulomb. A single electron has a charge of about -1.6×10-19 C. So that would mean your wire is missing about 520 electrons.
Any number of electrons you can count is too small to be felt without sensitive instruments. You need more charge.
Try rubbing a balloon on your hair. You can get the balloon to stick to the ceiling if it's not too humid. And you have hair :)
If you can find a CRT monitor or TV, try that. They work by shooting a lot of electrons at a screen of phosphors. When you turn them off they retain some of that charge. You can sometimes get bits of paper or dust to stick to them. You might feel the forces on your arm hairs held closely.
Or get your hands on a Van de Graff generator. One of these can charge a metal sphere many orders of magnitude more, and you will have no trouble feeling the forces then.
