How Does a Coaxial Cable's Capacitance Change with Different Configurations?

[bdubb427]

Help please w/ the following questions

Homework Statement

1.
A coaxial cable is given with two concentrically placed dielectrics. What is the capacitance of this structure? If an ungrounded metal shell is placed at a certain distance from the inner electrode, what will be the capacitance now? Plot the magnitude of field and potential as a function of radius in both cases.

Homework Equations

C = Q / V = [2 * pi * epsilon * length] / [ln(b/a)] where b is the radius of the entire cable (outer and inner conductor) and a is the radius of just the inner conductor

Homework Statement

2. A charged spherical shell is placed 1m above a ground metal plate. Find electric field.

Homework Equations

besides coulomb's law, i don't have any other relevant equations for this.


Our textbook is really hard to understand, and the examples given in the text are even harder to follow. the book is Fundamentals of Applied Electromagnetics by Ulaby.. Any suggestions for another book are nice, but my exam is coming up and finding another book is just not an option at this point. Please help if u can. thank you...

 

[JoAuSc]

For problem 1, you have four layers: a charged conducting cylinder, an inner dielectric layer, an outer dielectric layer, and an outer conducting shell. Because you have two dielectrics, the equation you provided (with just one epsilon) won't work. You'll need to rederive that expression for two dielectrics. I believe this would require a.) finding the electric field in the presence of a dielectric, which might be as simple as switching epsilon_0 with epsilon_1 in region 1 and epsilon_2 in region 2 (however you decide to label them); b.) calculating the voltage differences between the boundaries from the electric fields; and c.) calculating Q/V. I am not sure if adding in a thin metal shell would make any difference.

The second question seems much easier. First, with the method of images we know that this problem is equivalent to one where we have two spheres with opposite charges which are 2m apart. Gauss's law gives you the E-field for each sphere in the absence of the other sphere, and by the superposition principle you just add their fields to get the total.