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Electric Field Direction Significance !

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I am confused about the electric field lines which are depicted mostly on the Internet as per conventional way.

What I understand that the conventional current was due to positive charges which was wrong. Actual flow of the current was due to the negative charges or electrons. When the conductor is connected with both terminal of the battery Positive ( Where the concentration of the positive charges are more) and negative (Excess of electrons or negative charge) charges the electric field is generated. Electric field itself  is the influence of charge around it. Since there is net positive charge on one electrode of the battery and net negative charge on the another electrode, Electric field is generated around the electrodes. Now we have the property of the charges that similar charges repel and different charges (+ and -) attract each other. Since due to electric field influence and this property of the two different polarity charges attract the electrons started drifting from negative to the positive terminal of the battery due to force of attraction from the electric field. Correct me if I am wrong some where. 

Now main problem is when I see the direction of electric field  on the internet it is the convention from positive to the negative. this is really confusing me because as per force influence by electrons due to the polarity causing the electrons to flow from negative to positive terminal but the direction which is mentioned is from positive to negative. How is that possible that force direction is different and the particle which moved due to that force is in different direction ?

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I understand you problem. The electric field is always pointing from the positive potential to the negative one. So you have an electric field vector. But: the force is the known Lorentz force which is (without a magnetic field): F=q*E . Since q is negative in the case of the electron, the electron moves against the pointing direction of the electric field.

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The positive to negative convention predates a good understanding of the atom... It is best to think in terms of hole flow and electron flow. Hole flow being the "flow" of the "holes" left in the valence of atoms and opposite to electron flow.

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