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Suppose we have conducting metal cube and we give a positive charge $Q$ to it.

Now giving positive charge simply implies taking away electrons from that small region , so when we take away electrons the electric field created due to increases positive charge density attracts electrons till the charge reached the surface.

Now we have net charge on the surface but how will this be distributed , I mean whether it will be uniformly distributed or not.

I think it should be uniformly distributed so that the charges are at maximum distance from each other but in actually it is non-uniformly distributed.

How does this happens?

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It would be uniformly distributed if the conductor was a sphere but in case of cube there occurs high charge density at corners, thus the charge will be non uniformly distributed. As surface charge density is inversely proportional to area, area at the vertices minimizes to point sized thus charge density is high there. Take this image as an example enter image description here

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