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

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The discussion focuses on calculating the electric potential inside and outside a long cylindrical shell with a uniform surface charge distribution, where the upper half has a charge density of sigma naught and the lower half has a charge density of -sigma naught. Participants are encouraged to show their calculations for verification. The electric potential is influenced by the distribution of charge, leading to different values inside and outside the cylinder. Theoretical concepts related to electric fields and potentials in cylindrical coordinates are also referenced. Overall, the thread aims to clarify the relationship between charge distribution and electric potential in this specific geometry.
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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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