Professor M.A. Lieberman
Professor S.E. Schwarz
Wilson Lee and Tim Chou

    Electrostatics is an area of electromagnetics that involves constant voltages. In most cases, slowly varying voltages can be analyzed using electrostatic approximations. In this lab, we will analyze several electrostatic configurations including the parallel plate capacitor, the coaxial cable, microstrips over a grounded plate, two opposing potentials utilizing the method of images, and a stepped conductor over a plane conductor. This will give in-depth perspective into the concepts of electrical field, equipotential surfaces, capacitances, and the method of images.

    For this lab, we will utilize Matlab, a very powerful mathematics software, to approximate the various electrostatic configurations. The six files you will need are PARALLEL.M, COAX.M, MICROSTRIP.M, IMAGE1.M, IMAGE2.M, and STEP.M. To launch Matlab in Windows, go to either the Matlab icon in the START menu or a short cut on the desktop and click on it. Matlab will start and at the prompt, type ‘pdetool’ and hit ENTER. A new window will open for the Partial Differential Equations Toolbox. From here, you will open each file from the FILE menu. To obtain field and potential graphs for each configuration file, select PLOT SOLUTION from the PLOT menu. You may change the plot parameters to customize your graph. This will create the equipotential and electric field graphs necessary to observe each configuration below.

    For each configuration below, perform the specified tasks, and then compare your analysis with Matlab. All hand-sketched plots should be done before coming to the lab.

1. Below is a parallel plate configuration. Assuming that the top plate is at 10V and the bottom plate is grounded at 0V, sketch the equipotential surfaces and electric field lines for the following parallel plate capacitor.

2. Open the file PARALLEL.M in Matlab and observe the shape of the equipotential and electric field lines with Matlab.
3. Neglecting fringing, approximate the capacitance of the system assuming the plates have an area of 1cm, separation distance of 1 mm and permittivity of e =e _o=8.85´ 10^-12 F/m for the space between the plates. C =__________F

1. Sketch the equipotential and electric field lines for the following coaxial system. Assume an inner voltage of 10V and an outer voltage of 0V.

What shape do the potential lines take? Are they cylinders? Is the 5V surface midway between the inner and outer electrodes? What configuration do the field lines take?

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2. Open the file COAX.M in Matlab and verify the equipotential and electric field lines with Matlab.

3. Calculate the capacitance per meter of the coaxial transmission line assuming an inner radius of 1mm and outer radius of 5mm. The dielectric has permittivity e =e _o=8.85´ 10^-12 F/m. C=__________F/m

4. How is this related to the parallel plate capacitor? Does the coaxial system look like a parallel plate bent in a circle? Are there fringing fields? What property makes the coax cable more suitable for signal transmission than a parallel wire or parallel plate system?

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1. Below is a dual microstrip configuration. The top two strips are where the signal is transmitted. The lower plate is a grounded plate. Between the two regions is a dielectric with dielectric constant K (e =Ke _o). Assuming the two strips are at 10V and the bottom plate is at 0V, sketch the field distribution of the microstrip system if K=1.

2. Open the file MICROSTRIP.M in Matlab and verify the equipotential and electric field lines with Matlab. Do you observe crosstalk the fringing field effects? How do the fields appear between the two microstrips?

1. Sketch the field lines for the both diagrams below. The potential is at 0V on all surfaces except for on the small circle conductors specified.

2. How do the field lines appear on the left side of each diagram? Are they the same or are they different?

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3. Open the file IMAGE1.M and IMAGE2.M in Matlab and observe the equipotential surfaces and electric field lines with Matlab. Notice that the field lines are the same on the left side of the first configurations. This is the basis for the method of images. Why does this occur? What advantage does this property have in modern antennae engineering?    

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1. Draw the field and equipotential lines for the following stepped conductor. Assume the top conductor is at 10V and the bottom conductor is at 0V. Assume the walls on the left and right of the diagram are insulators.

2. Open the file STEP.M in Matlab and observe the potential and field lines.
3. Why do the potential and field lines take this shape? Are the field lines always perpendicular to the metal surfaces? How does the field vary at the ‘convex’ corner in comparison to the ‘concave’ corner? Are the fields stronger or weaker at the step in comparison to other areas in the region?

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