Electric Potential of Conducting Shell: R1 & R2, Q at Centre

The summary is: In summary, the potential at the surface of a conducting shell with inner radius R1 and outer radius R2 and a charge Q at the center is equal to (kQ/R2). This is because all the charge on a conducting shell is on the outer surface, and the charge Q present at the center induces -Q at the inner surface and +Q at the outer surface. Even if there is charge on the inner surface, it is canceled by the center charge, making the potential the same from the outer surface to the center. This is because potential can be seen as work done by the electric field, and since there is no field inside the shell, the potential is the same throughout. However, if the inner charge
  • #1
heman
361
0
In a conducting shell,with inner radius R1 and outer radius R2,and with charge Q at the centre,the Potential at surface is (kQ/R2),Why it is not (KQ/R1)?? :confused:
 
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  • #2
All the charge on a conducting shell is on the outer surface.
 
  • #3
Meir,
the charge Q present at the centre will induce -Q at the inner surface of shell and +Q at the outer surface of shell.
So obviously there is charge on inner surface too.!
 
  • #4
There are charge on inner surface but is canceled by the center charge, and there are charge Q distribute on the surface. So we can see the shell as a charged shell that charge Q is on the surface.
 
  • #5
brasil is right. I misread the original question, and didn't realize there was a charge at r=0.
 
  • #6
That's okay Brasil but howcome,the same potential for outer surface becomes equal to that of inner surface.!
 
  • #7
We can see potential as work done by electric field (albeit this "work" isn't the same as Force do) There's no field inside the shell, hence the potential is all the same from the outer surface to the center.
 
  • #8
brasilr9 said:
We can see potential as work done by electric field (albeit this "work" isn't the same as Force do) There's no field inside the shell, hence the potential is all the same from the outer surface to the center.
correctamundo

ps : do you guys know the charge distribution in the shell if the inner charge is not at the center of the sphere (let us say it is 1 cm away from the center to the left side)...what is the charge distribution in the shell ? is it uniform ? this is a classic... :tongue2:

marlon
 
  • #9
Of course it isn't uniform
 
  • #10
brasilr9 said:
Of course it isn't uniform

WRONG

marlon
 
  • #11
brasilr9 said:
We can see potential as work done by electric field (albeit this "work" isn't the same as Force do) There's no field inside the shell, hence the potential is all the same from the outer surface to the center.

Uh, if I'm visualizing this correctly, it's the same from the outer surface to the inner surface (since you're inside a conductor), but inside the inner surface, the potential goes as 1/r.
 
  • #12
marlon said:
ps : do you guys know the charge distribution in the shell if the inner charge is not at the center of the sphere (let us say it is 1 cm away from the center to the left side)...what is the charge distribution in the shell ? is it uniform ? this is a classic...

The charge distribution on the inner surface would have to be non-uniform in order for there to be an electric field of zero inside the conducting shell. However, the distribution on the outer surface would be uniform. Conductors essentially "hide" the information about the charge inside them and that's why the http://www.absoluteastronomy.com/encyclopedia/f/fa/faraday_cage.htm [Broken] works to block electromagnetic waves.
 
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  • #13
SpaceTiger said:
The charge distribution on the inner surface would have to be non-uniform in order for there to be an electric field of zero inside the conducting shell. However, the distribution on the outer surface would be uniform. Conductors essentially "hide" the information about the charge inside them and that's why the http://www.absoluteastronomy.com/encyclopedia/f/fa/faraday_cage.htm [Broken] works to block electromagnetic waves.


college application approved :approve:

marlon

ps : it has been a while, man, how have you been ?
 
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  • #14
marlon said:
ps : it has been a while, man, how have you been

Pretty good, just chilling in Seattle for a few weeks. :biggrin:
 
  • #15
SpaceTiger said:
Pretty good, just chilling in Seattle for a few weeks. :biggrin:
what exactly does chilling mean ? :wink:

is it a grunge thing ?

marlon
 
  • #16
marlon said:
what exactly does chilling mean ? :wink:

is it a grunge thing ?

Heh, I was a grunge freak in high school, but no, it just means I'm relaxing. But I guess that's not entirely true, since I'm here to work with an old advisor. :tongue2:
 
  • #17
SpaceTiger said:
Uh, if I'm visualizing this correctly, it's the same from the outer surface to the inner surface (since you're inside a conductor), but inside the inner surface, the potential goes as 1/r.

ops! I type to quick that I didn't notice I write the wrong thing. You are right.
 

1. What is the formula for calculating the electric potential of a conducting shell at the center?

The formula for calculating the electric potential of a conducting shell at the center is V = kQ/R, where V is the electric potential, k is the Coulomb's constant, Q is the charge on the shell, and R is the radius of the shell.

2. How does the electric potential change as the distance from the shell's center increases?

The electric potential decreases as the distance from the shell's center increases. This is because the electric potential is inversely proportional to the distance from the center, according to the formula V = kQ/R.

3. What is the relationship between the electric potential and the charge on the conducting shell?

The electric potential is directly proportional to the charge on the conducting shell. This means that as the charge on the shell increases, the electric potential also increases, according to the formula V = kQ/R.

4. How does the electric potential of a conducting shell compare to that of a point charge?

The electric potential of a conducting shell is similar to that of a point charge, but with some key differences. Both have a potential that decreases with distance, but the potential of a conducting shell is constant at the surface, while the potential of a point charge increases as you get closer to the charge.

5. What is the significance of the radii R1 and R2 in the formula for electric potential of a conducting shell?

The radii R1 and R2 represent the inner and outer radii of the conducting shell, respectively. These values are important because they determine the distance from the center at which the electric potential will be calculated. R1 is used for points inside the shell, while R2 is used for points outside the shell.

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