When we let the electron move freely in an electric field, the electric potential of electron must decrease but the electron moves opposite to the field so do we say that it's electric potential is increasing?
When the electron moves freely in an electric field, the electric potential of the electron increases, not decreases, and its electrical potential energy decreases. This is because high and low electric potential is defined by the convention that the direction of an electric field is the direction of the force that a positive charge would experience if placed in the field.
Based on this convention, a positive test charge placed in a field generated by another fixed positive charge will move in the direction of the field generated by the fixed charge, i.e., away from the fixed positive charge losing both electrical potential and electrical potential energy. On the other hand, if an external force moves the positive test charge against the direction of the field, i.e., towards the fixed positive charge, the electrical potential and potential energy of the positive test charge increases. So the location of the fixed positive charge is by definition high potential.
Now, if an electron is placed in the field, the field will move the electron in a direction opposite the field moving it toward the fixed positive charge. Since the location of the fixed positive charge is defined as high potential based on convention, the electron is considered to gain potential. On the other hand, the electron clearly loses electrical potential energy.
Hope this helps.
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