Line of charge and conducting sphere (method of images)

• thedddmer
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.
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

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.

vanhees71
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
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.

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.

Replies
6
Views
2K
Replies
3
Views
602
Replies
7
Views
2K
Replies
49
Views
4K
Replies
4
Views
2K
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
17
Views
492
Replies
2
Views
956