Solving [problem2.26]: A Conical Surface's Potential Difference

AI Thread Summary
The discussion revolves around solving a problem from Griffiths' Introduction to Electromagnetism regarding the potential difference between two points on a conical surface with a uniform surface charge. The integral required for the solution is noted to be complex, prompting requests for assistance. It is suggested to utilize spherical coordinates for simplification, as the integral does not depend on the phi component due to symmetry. Additionally, it is emphasized that integration must also account for the radial distance, dR, and to consult calculus resources for relevant integrals. Overall, the conversation highlights the challenges of the problem and offers guidance on approaching the solution.
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I have a problem from Griffiths Introduction to EM

[problem2.26] A conical surface (an empty ice-cream cone) carries a uniform surface charge <sigma>. The height of the cone is h, and the radius of the top is R. Find the potential difference between points a(the vertex) and b (the center of the top)

The integral is so complicated. Anyone has the solution?

Thanks a lot.
 
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Do the integral in spherical coordinates (r,theta,phi). The integral doesn't depend on phi (the phi components cancel out) and since r and theta are constant for the geometry of an ice cream cone, the integral is just over phi. Use the integral that takes you from the charge distribution directly to the potential.
 
Whoops,

You do need to integrate over dR as well. Look up that integral in the back of a Calculus book. You'll have to play around with it a little
 
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