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Suppose that there are negative charges (e.g. electrons) only. There are more negative charges on left than on right. How would electric field be constructed? (So, What would be the direction?) And how would electrons flow (because of electric field)? The text says that it flows from left to right, but I am not getting this.

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If there are more electrons on the left, then electrons will be repelled by the left side more than they are repelled by the right side and so will move right. – Jonathan. Jan 13 '13 at 16:01
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The electric field $\vec{E}$ builds up because of the misbalance of charge on the left and right side of your model. To a test charge $q$, which we place in the middle of the charge clusters, the left side cluster appears more negatively charged than the cluster on the right side. Thus you can already distinguish between the cathode (left, negative) and the anode (right, positive) of the system. What you constructed is just a very simple form of a capacitor. So your question is the same to: Towards which direction do electrons flow in a capacitor? The force on a test charge is $\vec{F}=q\cdot\vec{E}$. It is parallel to the electric field. But your question was concerned about the direction. One could try to answer it simply with the Coulomb force, which tells us that, equally charged particles are repelling. The anode will exert a less repelling force on the test charge than the cathode. Thus the direction is towards the anode.

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