How exactly does a battery produce a current in the circuit connected across its ends? I dont want to know the chemical reactions in the battery core, but just the essence of it. I believe it doesn't do this by creating an excess of electrons at the -ve terminal and a deficit at the positive terminal. Moreover, how is the voltage and the EMF different in their definitions and value. Electric field being a conservative field, can the work done in motion of electrons in the conducting wire and all the components be compared to the work done in any other path across the terminals of the battery? And on a side note, how can we theoretically derive an relation between the potential difference and the electric current?
Answer
The technical name for the structure in a battery is known as the "electrochemical cell". It consists of an electrolyte (or more of them), a liquid with ions that carry the electric charge. The asymmetry in the battery, the main reason why it works, is that these two types of carriers like to participate in chemical reactions in two different containers, near the two electrodes.
Positively charged ions – imagine $Na^+$ from salt, although it's not the most realistic example – like to to get "attached" to one electrode while the negatively charged ions – imagine $Cl^-$ ions from salt – like to get "attached" to the other one. These two types of reactions are called reduction and oxidation, respectively, according to the sign of the charge that the ion is gaining or losing. I don't want to get lost in sign errors so I haven't assigned them to the first sentence of this paragraph. As these chemical reactions are running, they are producing a charge asymmetry, and therefore a discrepancy between the potentials of the two electrodes, and this asymmetry is compensated by the flow of electrons through the wires of the circuits (outside the battery). In the long run, one is converting chemical energy (sort of an electrostatic potential energy of ions – they're "higher", using a gravitational analogy, before they react with the electrodes) to a hopefully useful energy done by the circuit. The total energy is conserved. The energy deposited to a charged particle moving across voltage $V$ is $E=VQ$.
EMF, the electromotive force, is a special type of voltage, so its SI unit is 1 volt, just like for any other voltage. I say it is a special kind of voltage because it is used for the "energy generating" parts of the circuits only, namely for batteries or parts that produce electricity by electromagnetic induction (following Faraday's law) like coils in a variable magnetic field. There's also voltage on resistors and capacitors but it's "passive", or "consuming" the power created elsewhere, so we don't count it as EMF. EMF is meant to be the "ultimate source of life" in electrical circuits.
Concerning the derivation of the relation between current and voltage, I suppose you mean Ohm's law $V=IR$. Its microscopic form is $\vec j = \sigma \vec E$, i.e. the current is proportional to the electric field where the coefficient $\sigma$ is known as conductivity. This formula holds for metals rather well because the electric field accelerates electrons up to an average speed dictated by the trade-off between the electric field acting on the electrons; and the decelerating speed from the collisions. This trade-off leads to a velocity that is proportional to $\vec E$ as well, and $\vec j$ is the product of the electron density and the average velocity of these carriers.
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