The actual question in my mind is that ……..at anode zinc oxidises to form $\ce{Zn^{2+}}$ and $2$ electrons, but it should be the same case at cathode because copper should also oxidise to form $\ce{Cu^{2+}}$ and $2$ electrons. Then in this case the potential difference is zero hence there is no current flow……please clarify?
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1Review the guide How to ask and Asking FAQs to prevent clarification requests, objections, downvoting or closure. – Poutnik Feb 07 '24 at 03:49
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1The Daniell cell is such a frequent topic on many sites involved in chemistry, including this one, that I have strong suspicion you have not done your searching homework before asking. – Poutnik Feb 07 '24 at 07:26
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I have done it already but i coulnt find it – Physics student Feb 07 '24 at 07:47
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To search this site: https://chemistry.stackexchange.com/search?q=daniell+cell A sample of results: https://chemistry.stackexchange.com/questions/175183/simple-cell-vs-daniell-cell Look up also definition of cathode and anode. – Buck Thorn Feb 07 '24 at 08:24
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I closed and then quickly reopened when I saw that my proposed duplicate is about a salt water cell with a different electrolyte. Similar principles hold though. – Buck Thorn Feb 07 '24 at 08:35
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This is closer to what you are asking: https://chemistry.stackexchange.com/questions/126644/copper-electrode-in-a-daniel-cell – Buck Thorn Feb 07 '24 at 08:38
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You may find useful reviewing of search results for site:stackexchange.com OR site:libretexts.org OR site:wikipedia.org OR site:hyperphysics.phy-astr.gsu.edu Daniell Cell schema – Poutnik Feb 08 '24 at 15:08
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Physics student is wrong for two reasons. First, in the Daniell cell cathode, copper is not oxidized. It is the contrary. It is reduced from $\ce{Cu^{2+}}$ to $\ce{Cu}$, and it is reduced by the $2$ electrons produced by zinc at the anode. Second, the potential difference is not zero. It depends on the concentration of the ions in solution. But it is usually around $1$ Volt.

Maurice
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The copper electrode is at a different potential from the zinc electrode. Also is the Daniell cell not designed to give a well defined voltage and its use restricted to a Wheatstone bridge environment of ZERO current draw, hence a constant voltage. This could be where the confusion is arising. – jimchmst Feb 07 '24 at 22:48