# Electric Charge

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

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

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

#### Attachments

• Infinite line of charge.jpg
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• Semi- infinite line of charge .jpg
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• ring of charge.jpg
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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

#### Attachments

• disk of charge page 1of2.jpg
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• disk of charge page 2of2.jpg
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• semi-ring or arc of charge.jpg
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