What causes electrons to move from the anode to the cathode in a galvanic cell?

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In a galvanic cell, electrons are supplied by oxidation at the anode. I am struggling to find clarity on what makes the electrons move from the anode to the cathode when a wire is connected between the two. I have come across some texts on the internet that say the electrons are attracted to the positive potential (cathode) but they say that it is not strictly true to say that the electrons are attracted to the positively charged cathode. This has very much confused me. I thought you can only have a voltage when net charges are involved. If you have a positive point charge in space, then at a distance r away from this charge there will be a voltage - say 8 volts. This means it would take 8J to move a 1 coulomb test charge from infinity to that point. I was taught this concept of voltage to be the definition of voltage. So, how can electrons move to the cathode when it is not a source of net charge, i.e. there are no negative charges attracting it? Or even, how can the cathode be a source of positive potential without the notion of net charge?
 
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There is net charge. If you place a piece of metal into water it will become slightly charged. Usually negatively since the metal dissolves i.e. it looses positive metal ions which leaves excess electrons in the metal. So if you place a piece of zinc and copper in a cup of water both metals become charged negatively but since zinc reacts more strongly it gets a stronger charge. So in total you have an electric field between the two metals and therefore a voltage. This is however simplified. There are more reactions happening e.g. oxygen at the copper electrode reacting with OH- ions.
 
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