Where Is the Line Image of a Charged Cylinder?

[Bobbo Snap]

Homework Statement

A long conducting cylinder bearing a charge \lambda per unit length is oriented parallel to a grounded conducting plane of infinite extent. The axis of the cylinder is at distance x_0 from the plane, and the radius of the cylinder is a. Find the location of the line image, and find also the constant M (which determines the potential of the cylinder) in terms of a and x_0.

The Attempt at a Solution

My instructor is giving us problems from a different book than we are using in class and there are some gaps in the material covered. That said, we haven't covered anything but point images (i.e., no "line images"). It seems to me that the location of the image would be at a distance -x_0 on the other side of the plane by symmetry. Is this correct? And I have no idea how to find M. Does anyone have any suggestions?

 

[Bobbo Snap]

Anyone? Am I correct in thinking that the image is on the other side of the plane? Any hints on how to to find M?

 

[TSny]

The line image is on the other side, but not at a distance $x_0$. The problem is rather involved, so you have some work cut out for you. You might start with finding some references on the method of images.

http://www.ece.mcmaster.ca/faculty/nikolova/4FJ4_downloads/tutorials/T02_CircuitParametersTLs.pdf I found that contains some discussion of the type of geometry in this problem. In fact, if you can follow the material starting on page 8, I believe you should be able work out the solution.

 

[Bobbo Snap]

Thanks, that does look like the geometry of this problem. I think the ratio \rho_1/\rho_2 is the constant M it's asking for but I'm not sure how the potential values were found. I will study it some.