Line of charge and conducting sphere (method of images)

In summary, the conversation discusses the potential of an infinite line charge and a conducting sphere. The possibility of using a point charge as an analog is mentioned, but it is noted that the situation is quite different from what has been previously seen. The alternative definition of a circle is also brought up, but its relevance to the problem is not yet clear.
  • #1
thedddmer
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Homework Statement
Need to use method find the geometrical place of the images and the charge density of an infinite line of charge and a conducting sphere
Relevant Equations
so the problem is only to find a segment of the line of charge inside the sphere, should be and kind of egg shape image (at least is what someone told me)
I was thinking of using the sphere and point charge as an analog, but is quite diferent from what i have seen
 
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  • #2
thedddmer said:
I was thinking of using the sphere and point charge as an analog,
OK

thedddmer said:
but is quite diferent from what i have seen
An infinitesimal element of the line charge can be treated as a point charge. Sketch a diagram of the situation and consider an arbitrary element of the line charge.
 
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  • #3
https://en.wikipedia.org/wiki/Circles_of_Apollonius

The alternative definition of a circle: the set of all points whose ratio of distances from two points is a fixed constant.

After all the potential of two (equal but opposite line charges) is

##\frac{\lambda}{2 \pi \epsilon_0} \ln \frac{r_1}{r_2}##

If that is a constant

then

##\frac{r_1}{r_2}## is also constant
 
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  • #4
PhDeezNutz said:
The alternative definition of a circle: the set of all points whose ratio of distances from two points is a fixed constant.

I'm having a hard time relating this to the infinite line charge and conducting sphere. I do find that the image curve is a circle.

But I haven't yet figured out how Apollonius' definition of a circle helps in this problem.
 
  • #5
TSny said:
I'm having a hard time relating this to the infinite line charge and conducting sphere. I do find that the image curve is a circle.

But I haven't yet figured out how Apollonius' definition of a circle helps in this problem.

Oh wow I totally misread the OP. I thought OP wanted to know the image of an infinite line charge inside a cylinder. And wanted to use the point charge image inside a sphere as an analog.

Welp.
 

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