Finding potential difference in a very long hollow cylinder

AI Thread Summary
The discussion focuses on calculating the electric potential difference in a long hollow cylinder with inner radius A and outer radius B, given a uniform charge density p. The user initially applied Gauss's law to determine the electric field at a point R, leading to an integration from 0 to A+D, resulting in an incorrect potential difference expression. The correct potential difference is identified as -p/2E0 (4A^2/2 - A^2/2 - A^2ln2). Participants are encouraged to share their calculations to clarify the discrepancies in the user's approach. The thread emphasizes the importance of accurate integration and understanding of electric fields in cylindrical geometries.
aldofbg
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A very long hollow cylinder has inner radius A and outer radius B. It has a known unit charge per unit volume p. Find the difference in the electric potential a point on the axis and a point a distance A+D assuming A+D<B
The diagram is in the url. It is #3
http://people.physics.tamu.edu/etanya/P208/exam_2_2014.pdf

I used Gauss law to find the Electric field at a point 'R'. I got pV/E0 then I integrated this from 0 to A+D and I got the answer p[A+D]^2/E0 though this isn't the answer. Could someone explain what I did wrong?
The correct answer is -p/2E0 (4A^2/2 - A^2/2 - A^2ln2)
 
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aldofbg said:
I got pV/E0
Please post your working to that point.
 
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