I'm doing Grade 12 Chemistry and I'm unsure of this, taking the hydrogen electorde as having a potential of 0 volts.
I'll use the copper-zinc cell as an example. Just let me know if I've got the full logic right:
Zinc has higher electronegativity, so due to the equilibrium $\ce{Zn <=> Zn^{2+} + 2e-}$, we have more charge building up in the Zinc electrode than in the Copper electrode. (Given both half-cells are of same concentration and in same temp)
We have a potential difference between the two electrodes. This means some charge from the Zinc electrode will move to the Copper electrode in such a way that both electrodes will momentarily have equal charges.
Since the charge in the Copper electrode has gone up, we have added electrons to the equilibrium reaction $\ce{Cu^{2+} + 2e- <=> Cu}$. We therefore create more copper.
Is this why an electrode with a higher potential will "pull" the electrons from the electrode with a lower potential?