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

[question2004]

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.

 

[sinyud]

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.

 

[sinyud]

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