Capacitance of a cylindric capacitor (only a piece)

[henry7512]

Hi..
I´ve been trying to solve this problem for a couple of weeks and I need fresh ideas...it´s a 30 degree piece of a 10 cm high cylindric capacitor..how can I calculate its capacitance if it stopped to be symmetric?From my point of view the field between the 2 plates shouldn´t be calculated the same way we use for the cylindric capacitor..anyway..if the field can´t be calculated that way then I think it gets to complicated to do it...
Thanks for any idea (as long as it´s good)

 

[Bob S]

This is a good question. If the field gap is very small relative to the other dimensions of the capacitor plate, the fringe field is small, and you can use a parallel plate capacitor approximation, or use the cylindrical capacitor solution for a 360 degree capacitor, and divide the capacitance by 12. As a last resort, look at the problems at the end of chapter 4 in Smythe "Static and Dynamic Electrricity" 3rd Ed. for problems that calculate the edge correction for bulging fields.

 

[henry7512]

thanks Bob..that was very kind of you

 

[Born2bwire]

If you want to go all out you can also try a method of moments solution. Harrington's book or Gibson's book both give good details on how to solve electromagnetic and electrostatic problems using the method of moments. They both have the problem of a charged plate. This solution will take into effect things like fringe fields and such but will be much more involved than the approximations that Bob has suggested.