EM Problem: Floating Conducting Cylinder

[jegues]

Homework Statement

See figure attached.

Homework Equations

The Attempt at a Solution

Originally I have solved this problem using Gauss's law by defining a gaussian surface in the form of a cylinder around the floating cylinder to get the electric field distribution underneath the cylinder to ground.

The result I obtained was,

$$V(y) = \frac{Q_{pul}}{4 \pi \epsilon_{0}}\left( \frac{ln(d-y)}{d} \right)$$

but since we aren't told what Qpul is we cannot plot the variation of the voltage.

My professor suggested I try solving this problem using image theory and laplaces equation in cylindrical coordinates in order to avoid Qpul.

Can someone explain to me how this done?

Thanks again!

 

[rude man]

My professor suggested I try solving this problem using image theory and laplaces equation in cylindrical coordinates in order to avoid Qpul.

Can someone explain to me how this done?

Thanks again![/QUOTE

Problem with Gaussian surface is, the charge is not uniformly distributed so you can't take advantage of symmetries.

The image is a similar conductor of opposite sign a distance d below the ground.

This is a real bear of a problem. What you want is the capacitance between the cylinder and the conducting plane, i.e. the capacitance between the cylinder and its image.

Do you use Jackson?