Line of charge and conducting sphere (method of images)

[thedddmer]

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

 

[TSny]

I was thinking of using the sphere and point charge as an analog,

OK

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.

 

[PhDeezNutz]

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

 

[TSny]

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.

 

[PhDeezNutz]

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.