Are the Earth wire and the Neutral wire the same? I have a physics book which says that the earth and the neutral wire in a socket are joined at the city substation so that they are at the same potential, indicating that one can easily put a plug in the socket between the live and the earth wire instead of the neutral wire.
One of my teachers says that the earth and the neutral wire are not the same. According to him, if a very low power bulb (about 1W or 2W, or even less) is connected between the earth and the neutral wires, then the bulb glows,  suggesting that the neutral wire has some potential.
I haven't tried this experiment.
Can anyone please explain the reality?
 A: This is really an Electrical Engineering but seeing as you and I are here I'll have a go with an answer.
It is pretty well universally true that any electrical socket outlet in a domestic property intended to be used to plug in a variety of consumer appliances will have 3 connections; Line(live), Neutral & Earth. It's becoming standard practice in electrical wiring installations to call the "hot" wire the "Line" now instead of the "Live" so I will stick to that so we can get used to it if you want to read further, e.g. Wiring Regulations Handbooks, etc.
The power for the appliance is supplied via the Line and Neutral connections. The current will, under no fault conditions, be the same. If a 10 Amp supply current is flowing through the Line conductor then 10 Amps is also flowing through the Neutral conductor (for that one socket/appliance).
The purpose of the third connection, the Earth conductor, is ONLY for safety.
Specifically to reduce or eliminate the possibility of a harmful electric shock AND the possibility of an electrically ignited fire. Many domestic electrical appliances have a case made of metal, this includes items like a convector heater, a fridge, a microwave oven and so on. The case is metal for structural/design reasons (not electrical reasons). For example a plastic cased convector heater might be a very silly and dangerous idea (think about it !). IF we have a metal case it is possible, in the event of an internal fault, for the case to become electrically live and thus impart an electric shock, possibly fatal, to anyone touching it. We therefore connect the metal case to the earth wire of the socket using one separate core of the 3 core flex. The appliance is then "earthed".
Consider now what happens with a faulty appliance. Some electrical current due to the internal fault can flow through the earth wire of the electrical installation back to the source (e.g. if earth and neutral are connected at substation as you say). We can detect this current in the earth wire as a "fault condition" and trip the circuit thus removing the supply and alerting the user to the possibility of a fault. In modern type installations which include an Earth Leakage Circuit Breaker (aka RCD or RCCD) the detection of earth fault current flowing in the earth wire is very fast (< 40mS).
You should under no circumstances attempt to connect a load of any kind between a line conductor and an earth conductor. Neither should you attempt to connect a bulb or anything else across the neutral and earth conductor. In fact it can be dangerous to even use a cheap multimeter to measure voltages on your domestic electrical installation wires (they are not rated for the impulse voltages that may appear on the mains sometimes). By all means read about domestic electrical wiring systems but do not experiment on them ! I once saw someone attempt to measure the internal resistance of the mains using an AVO on the low ohms range while I was in school in the physics lab. The results were not pretty, luckily it was only the AVO that was an irrepaiable heap of black gunge not the human involved. He had a lucky escape.       
A: The earth (ground) wire and neutral are both ideally at the same zero volts. They are connected together somewhere nearby (depending on your local safety rules)
The idea of the the earth wire is that if somehow the live wire touches the case of the gadget the electrcity flows to earth through the earth wire (and with enough current to blow a fuse) rather than through you.
Most of the time there is no current flowing in the ground wire and so it is very close to zero volts. But there is current flowing from the appliance through the neutral wire and so because it has some resistance it will be at some small voltage (remember V=IR). You can measure this voltage or use it to light a bub.
ps  don't try this at home, it is dangerous if you manage to disconnect the neutral leaving the appliance connected only to live 
A: If you connect a lamp (don't do it) between the line (live/active) and earth current will flow through it.  Essentially energy is flowing from higher potential to lower potential.
The earth could be the earth pin of the socket outlet, an earthed water pipe, even a metal stake like a screwdriver stuck into the ground.  If the circuit has a safety switch (RCD/Earth Leakage device) it will trip.  Probably the reason  a 1 Watt bulb was suggested was that the current flowing through it will be less than the trip value of the RCD.
Most (but not all) reticulation for mains electricity have the neutral and earth connected together for safety reasons.  Lets say your electric stove or refrigerator or toaster becomes faulty and the live conductor is touching the metal of the appliance.  The metal is now at Mains potential and a person touching it effectively "becomes the light bulb", that is, current will flow through them to earth and potentially kill them.
The earth conductor connected to the metal of the appliance now becomes the return path for current as it is connected to neutral, usually in the switchboard. Current follows in this path of lower resistance, rather than through the person.  Usually the fuse will blow or circuit breaker will trip, especially if the fault is a short circuit.
Unless you are properly trained with all the right safety precautions in place, please do not experiment with mains electricity. Electricity kills many people each year, very often through no fault of their own.  Any faulty wiring, incorrectly installed protective devices or combination of circumstances could mean that protective devices do not function as intended, when intended.  If, despite all the warnings you do choose to experiment, then I hope you haven't yet had the chance to pass on that gene!
