[ShubhamRathi]

My question is no Homework question. It is a wake up call to me and hopefully to the others whom I have tormented with this question.
My question is simple: Why does Anode have a positive charge and Cathode have a negative charge ( in an electrolytic cell)?
People have this gross misunderstanding that the charge is because of being connected to the positive and negative terminals of the battery.
That's completely untrue.
Battery cannot provide charges in a circuit.
Battery can only give potential difference that the free electrons of the metal begin to move from a path of higher potential to a path of lower potential.
If the batteries happened to throw charges in a circuit, Conservation Principle would be violated.
So the scheme is such:

The battery, provides the potential difference. The electrons begin to move along the path of potential difference.
To complete the circuit, they move from the electrolyte NaCl enter the cathode and return to the path of no potential difference ( the negative terminal)
Here everyone says that since Anode is positive and Cl is negative, Cl goes to Anode and Vice Versa for Na+.
But, As you understand- there is no way that any kind of charges are developed.
What is Amiss?

Why haven't people asked something so fundamental?

Say for one moment I even assume that Battery introduces charges in the circuit. That still doesnt explain why the Anode and Cathode have charges. Its obvious that the battery causes motion of electrons. And for charge to be developed, the charges have to be static on the electrodes. But that's not at all happening.

Thus, on either sides there is no reason why Anode and Cathode are charged. Any takers for this dilemma?

[Borek]

Oh my, you have just proven batteries don't work. What are we going to do? 

Seriously, when you put piece of metal into water, some of the atoms on the surface will leave the metal as ions, and the metal itself becomes charged. Now call this piece of metal an electrode.

Also, when you put a piece of metal in a solution that contains ions (of this metal, or other metal), some of these ions will get reduced on the metal surface, charging the metal. Now call this piece of metal an electrode.

Which process prevails and what is the equilibrium state is another question, and if you think about it for a moment you will realize it is in fact the same process in both cases, just running in the opposite directions.

[ShubhamRathi]

What prompts the metal ions to leave their stable metal ( uncharged) state and form ions?
And, It'll be great if you can tell me the scene at Cathode ( Why negative ions build up)

[Borek]

What prompts the metal ions to leave their stable metal ( uncharged) state and form ions?

In solution they are stabilized by solvation. And they love it enough to leave the metal. In small amounts, but you don't need a lot to build a charge required for single volt potential difference typical for a single cell of chemical battery.

And, It'll be great if you can tell me the scene at Cathode ( Why negative ions build up)

I already did. You don't need negative ions - all you need is that the charge leaves or enters the metal. When you grab electrons from the electrode (or add cations on the surface) - it becomes positively charged, if you introduce electrons (or remove cations) it becomes negatively charged.

[ShubhamRathi]

Hey Dude, With a hands on start with your reply, I finally got the right concept here: http://www.youtube.com/watch?v=tZK6l1vvPY8

[Cerebellum_Before_Thought]

From what I understand, a battery contains an inherent potential difference from its materials, and when a path is connected, the electrons move.  Your picture is misleading, unless I am mistaken.  That battery would expend its energy across the electrolyte.  A salt bridge needs to seperate the anode/cathode.  And then the electrons can be tunnelled through the wire and ending like a dud by putting a measely chloride ion into solution... that's where I believe the electron goes.  So, the cathode is rolling out electrons, which get absorbed by the nearest atoms, and an electrical gradient ensues.  The negative forces repel electrons at the anode, polarization occurs, and the batteries electrons are forced into the metal ion.  This ion follows its original electrons as they conduct into the anode, absorb the battery's electrons, and deposit as a metal.  Chlorine gas at the cathode can form because 2 chloride ions got jammed-up with electrons, and found themselves with an extra bond of electrons, which it was glad to force on to the next atom.  I could be arse backwards, though, lol, I hope it makes sense.  And the salt bridge would force the electron through the wire, ending up inside of a metal atom... and pulling off a positive ion from the salt bridge.  Anyways, have fun correcting my mistakes.

[Cerebellum_Before_Thought]

Dear lord, so the metal gets deposited on the cathode, and the anode gets the electrons and form at the anode, in a battery without a salt bridge.    And if a saltbridge is in place, the anode would absorb the electrons from the wire and deposit ions as a metal, while the cathode would release the gas... If someone can clearly straighten this mess out, I would appreciate it.  I think I got it, but electrochem was always hard to visualize.

[Arkcon]

The first thing you should do is try to isolate in your mind a battery and an electrolysis cell.