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== Permanent Materials ==

- 6061 3/8" Al rod stock<br>
- Teflon<br>
- Glass microscope slide<br>
- HP Signal Generator (DC-1 GHz)<br>
- Oscilloscope (at least 1GHz bandwidth)<br>
- Miscellaneous electrical components <br>

== Materials to Borrow When Necessary ==

- Milling machine<br>
- Lathe<br>

== Activities ==


=== Reading ===
# Read the Wikipedia articles on [https://en.wikipedia.org/wiki/Permittivity permittivity] and [https://en.wikipedia.org/wiki/Permeability_(electromagnetism) permeability]. With the help of the instructor or TA try to achieve a physical understanding of just what the permittivity and permeability mean in a bulk material.
# Read the first three sections of [[Media:Measuring_the_Permittivity_and_Permeability_of_Lossy_Materials_-_Solids,_Liquids,_Metals,_Building_Materials_and_Negative-Index_Materials_.pdf |this paper]] (pages 1-27). Pay particular attention to the permittivity (<math>\epsilon</math>) / capacitance and permeability (<math>\mu</math>) / inductance associations.

=== Permittivity of a ''Lossless'' Material From a Capacitance Measurement ===

[[File:Epsiloncap1.png |right |350px]]

# Place three samples (air, Teflon, glass) between the aligned and polished ends of two 3/8" diameter, 1/2" lengths of 6061 Al rods (as shown at right). <math>d</math> should be on the order of 1 mm. Measure the capacitances and, from the known surface area <math>A</math> and spacing <math>d</math>, determine the material's relative permittivity.  <math>C = \epsilon_r \epsilon_0 \frac{A}{d}</math> (for a capacitor with no fringing fields).
# How do your measured permittivity values compare to standard reference values?
# [https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html Use this web applet to build a capacitor and observe the field lines ]. Are there fringing fields?
<math>\epsilon_r</math>(air): 1.000536<br>
<math>\epsilon_r</math>(Teflon): 2.1<br>
<math>\epsilon_r</math>(glass): 3.7-10<br>

=== A Better Permittivity-Capacitance Measurement of a ''Lossless'' Material ===

[[File:Epsiloncap2.png |right |350px]]
# [https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html Use this web applet to build a ''guarded-electrode'' capacitor (as shown at the right) and observe the field lines ]. Are there fringing fields?
# Measure the three permittivities (air, Teflon, glass) again using this guarded-electrode setup.
# How do these results compare to your first (unguarded) measurements?
# How do these results compare to the standard values?

The measurements above for a lossless material amount to requiring the permittivity to be real (as opposed to complex). However, for a lossy material, the permittivity is complex and we need an additional characteristic (beyond simply the capacitance) to characterize the material. This additional characteristic is the conductance <math>G</math>. The measurement below will include the conductance of the material.
<br><br><br><br><br><br><br><br><br><br>

=== Permittivity of a ''Lossy'' Material From a Capacitance Measurement ===

# Employ the guarded-electrode setup above and measure the lossy material's capacitance and conductance. <math>C=\epsilon^'\frac{A}{d}</math> and  <math>G=\omega \epsilon^{''} \frac{A}{d}</math>, where <math>\epsilon^'\text{/}</math><math>\epsilon^{''}</math> are, respectively, the real and imaginary parts of the complex permittivity.