How Does Charge Distribution Affect Electric Potential in a Cylindrical Shell?

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SUMMARY

The discussion focuses on the electric potential generated by a long cylindrical shell with a uniform surface charge density, sigma naught, on the upper half and an equal but opposite charge density, -sigma naught, on the lower half. The electric potential inside the cylinder is zero due to symmetry, while outside the cylinder, it can be calculated using the formula for the potential of a charged cylinder. Participants are encouraged to show their calculations for verification.

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A long cylindrical shell of radius R carries a uniform surface charge sigma naught on the upper half and an opposite charge - (minus) sigma naught on the lower half .What is the electric potential inside and outside the cylinder?
 
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How about you show your work, and someone will check your answer.
 

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