What is the relation that links .m.f., current and electrons flow? I'm asking this question because I'm a little confused about this topic. So, I know that the current (conventionally) in a circuit flows from the positive to the negative pole, and inside the cell current flows from the negative to the positive pole with a loss of energy. If I consider the electrons flow everything works in the opposite way: in the circuit electrons from - → to + ; in the cell electrons from + → to - 
The problem is that I don't undestand why energy is spent to make electrons flow from the + pole to the - pole inside the battery, I mean that's the actual direction of the electric field (+ to -). I'm confused because a professor explained that energy is spent inside the battery because the current goes from - to + while the field from + to - which means that they go in opposite directions and thus energy must be spent to go against the field but current direction is just a convetional direction and not a physical direction! It does not make any sense to me.. 
Could someone be so kind to explain this concept to me? I will be really grateful. Thanks in advance and have a good day :) 
p.s. the confusing explanation can be found in the first two minutes of this video if someone is interested : https://www.youtube.com/watch?v=qWiltlnBxHQ
 A: Going back to the analogy given by Professor Lewin where he briefly describes the action of a Van de Graaff generator.  
An uncharged conducting dome is separated from the ground using an insulator.
Near the ground negative charges (electrons) are sprayed onto a conveyor belt made of an insulator.
The electrons travel towards the conducting dome.
The electrons leave the belt and move onto the dome which now has a net negative charge.
The potential of the dome is now less than that of the ground and an electric field exists in the region between the dome and the ground.
The direction of the electric field is from the ground towards the dome.  
As more and more electrons are collected by the dome the electric field gets stronger and stronger and the potential difference between the dome increases.  
To get the electrons to move from the ground to the dome (negative potential relative to the ground) requires work to be done and that work is done by whatever is making belt move.  
It could be you moving the belt using the chemical energy stored in the food that you have eaten, a motor using electrical energy, a water wheel using the gravitational potential energy, etc, and as a result of the work done moving the belt is an increase in the electrical potential energy stored in the Van der Graaff generator.  
Now imagine a situation where the force between the electrons and the belt and the electrons on the dome is so large that the belts stops moving because whatever has been moving the belt cannot evert enough force to move the belt.
(If you have ever seen a demonstration which uses a Van de Graaff generator you may have noticed that the belt slows down as the charge on the dome increases due to the increased difficulty in moving charges onto the dome as the charge on the dome increases).
You now have the dome at a constant negative potential relative to the ground and no electrons are moving.  
Hopefully you can understand the analogy of this process with that of a pump moving electrons from one place (the ground) to another (the dome) and the pump having a finite capability in terms of setting up a maximum (constant) potential difference (pressure difference) between the ground and the dome.  
So overall there is a conversion of some form of energy into electric potential energy using a "pump" which moves the electrons.  
Note that this pump moves the electrons in the direction of the electric field set up between the ground (positive) and the dome (negative) which is opposite to the direction you would normally expect them to move.  
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An equivalent thing happens in a cell with the “pump” powered by chemical energy and that pump moving electrons from one terminal (which we call the positive terminal = deficit of electrons) to the other terminal (negative terminal = surplus of electrons) until such a time that the electric field between the positive plate and the negative field is so strong that the electro-chemical reaction cannot move any more electrons in the same direction as the electric field (from the positive terminal to the negative terminal).
There is then a steady potential difference between the terminals of the cell which is called the emf of the cell.
There is also an electric field set up outside the cell between its terminals (in a direction from the positive terminal to the negative terminal) but no current flows because air is an insulator (it contains no mobile charge carriers).  
If a conductor, which contains mobile charge carriers, is placed between the terminals of the call then electrons move from the negative terminal towards the positive terminal (in the opposite direction to that of the electric field which has been set up in the conductor).
The electron pump in the battery moves electrons from the positive terminal to the negative terminal to make up for the electrons which have left the negative terminal and travelled outside the cell to the positive terminal and in doing so keeps the potential difference between the terminals of the cell constant.  
A: There exist different types of so-called charge-carriers, for example:


*

*negative electrons as we see in metals,

*positive protons as we see in plasmas,

*positive holes as we see in p-type semiconductors and

*both positive and negative ions as we see in solutions where atoms are losing or gaining electrons.

*etc.


The usual case we think of is metallic wires, and that is why you think of electrons, but there are many possibilities. The lucky thing is that all charge-carriers are either positive or negative and they therefore always move exactly opposite of each other.
This is the key thing. Because imagine an electric circuit consisting of metallic wires reaching a set of semiconductors, continuing into an electrolytic bath containing ions etc... We have a mix of charge-carriers depending on where we look. It would be confusing to have to know the specific charge-carrier type everywhere. Instead, it has been decided that we just always talk as if the charge-carrier is positive.
After all, a positive charge-carrier moving leftwards and an electron moving rightwards give the same result. They both correspond to positive charge flowing leftwards. So such a decision was made in the past. A consensus to simplify how to talk about circuits. And this consensus covers everything from current direction over potentials and voltages to the directions of electric fields.
So, if you know that you are dealing with electrons in your specific case, then you must flip it all around in your head. A point at low potential is in fact high potential for the electron. The $+$pole on a battery is a point of high potential for a positive charge but of low potential for the electrons. 
Electrons therefore do not want to move through the battery from the $+$ to the $-$pole - that requires some huge effort done by the chemicals inside the battery. The chemical forces do work on these electrons to carry them to the $-$pole, and from there they will start flowing away from the $-$pole, through the circuit and back towards the $+$pole again.
In this way the battery supplies energy in the form of work to move charges against their will, and this work is "stored" by having the electrons "trapped" at a place they do not want to be add. This "stored energy is then released as they travel through the circuit and delivered to circuit components along the way.
