Deriving Electric Charge: Line, Ring, Cylinder, Cone, Sphere & Shell

[Chris W]

Hi all. I need some help.
Without using Gauss's Law, I have to derive the formula for the electric charge for different cases.
-I already did few cases such as:
1. Infinite line of charge
2. Semi - infinite line of charge
3. Ring of charge
4. Semi - Ring of charge or any arc of charge
5. Disk of charge
6. Infinite Sheet of Charge

-I need to derive:
7. Cylinder of charge
8. Cone of charge
9. Sphere of charge
10. Shell of Charge

I know that the basic "building block" for cases 7-10 is the ring of charge which I already have. Basically what I need is the setup of the integral for cases 7-10.

Thank you

Chris W

 

[maverick_starstrider]

It's just an exercise in different coordinates. A cylinder has constant r, varying z and phi/theta in cylindrical coordinate, a cone has varying z, r and phi/theta in cylindricalm a sphere has varying, r, phi, theta in spherical and a shell has constant r, varying phi, theta in spherical

 

[Chris W]

Thanks!

Yeah. Looks like I have all I need now I just have to set up the integrals.

Thanks! wow that was quick ... lol


please see what I have so far ... I hope all is good!

Thank you one more time

see attachment

 

[Chris W]

Thanks!

Yeah. Looks like I have all I need now I just have to set up the integrals.

Thanks! wow that was quick ... lol


please see what I have so far ... I hope all is good!

Thank you one more time

see attachment

View attachment 14354

View attachment 14355

View attachment 14356

 

[Chris W]

this is the rest of what I have so far

sheet of charge can be viewed as the disk of charge and letting the R go to the infinify