Electric Field Plotting Spring 2019 MQ PDF

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Electric Field Plotting Introduction and Theory: Text reference: Young, Adams, and Chastain §§17.6 -17.8 By definition, the electric field E is the force on a test charge divided by the amount of that charge. Because these forces are very small, we use the relationship between E and the electric potential V in order to measure the electric field. The electric potential is related to the energy required to place electric charges in some given configuration. The energy of an electric charge in a potential field is simply its charge multiplied by that potential. The electric field is a vector. This means it has both a magnitude and a direction. The magnitude of the electric field is proportional to the rate of change of potential in space. Its direction at some point in space is the direction of the force that would be exerted on a positive charge placed at that point. The faster the potential changes, the larger the field. For a two-dimensional field as in the lab setup, the electric field is given by the following equation: E=–

∆V

(1)

∆r

where E is the vector which points in the direction of the steepest change in the potential with distance r. You will measure the electric potentials and fields that occur in the plane of slightly conducting paper which models a 3D system as a cross section of the field in space perpendicular to the electrodes.

Objectives: To determine the equipotential lines and the corresponding electric field lines for a variety of arrangements of conductors in a plane. Equipment: Water tank; two types of electrodes (parallel lines as an equivalent to parallel plate capacitor and two concentric circles as an equivalent to coaxial cylinders); AC signal generator; digital voltmeter with single probe and fixed spacing leads; Vernier calipers. Procedure: Adjust the bars symmetrically in respect to the solid horizontal and vertical lines as well (see instructions). Connect the AC signal generator to the two electrodes submerged in water and set the sinewave shape signal with frequency f = 200 Hz and with maximum amplitude. (A) Measuring the electric field of parallel linear conductors (see Fig. 1). •

Using the single lead probe measure the potential of a number of equally spaced points in Page 1 of 4

between the two electrodes. Record the voltage measurements from the DVM directly on a sheet of paper that is a copy of the investigated system.

Power Supply +

Single lead probe x

DVM

-

+

Figure 1. Setup for measuring electric potentials and electric fields for parallel plate geometry. •

In GA make a graph of V vs. x. What does the slope of the linear fit represent?

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Using a ruler measure the separation between the parallel “plates”. Also, using the DVM measure the potential difference between the “plates”, then calculate the theoretical value of the electric field between the “plates”. How does this value compare to the slope you determined above?

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Make measurements to find a few equipotential lines, do this by repeating the above steps, but start from a different location between the “plates”. Draw these equipotential lines on the same paper as used above. Follow the equipotential lines for a short distance outside of the area between the parallel “plates”.

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Now make measurements of the potential along the “plates”. Does the potential in this region follow an equipotential line? Is this consistent with what you know about conductors?

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Switch to the probe assembly with a fixed spacing and measure the electric field directly at several points along an equipotential line in between the two electrodes as defined by equation (1). Remember to measure the spacing between the probe tips. Record the direction and magnitude of the electric field you determine by the use of little vectors on the same sheet as used above.

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Is the value of the electric field determined with this method consistent with the value obtained from your plot of V versus x?

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Is the direction of the electric field perpendicular or parallel to the equipotential lines?

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Now determine the direction of the electric field at the location of one of the “plates”. Is the direction of the electric field here consistent with what you know about conductors?

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Is the electric field between the “plates” uniform?

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Examine also a few points outside of the space in between the electrodes. Explain any trends or observations you made about the electric field in this region.

(B) Measuring the electric field of two concentric circles (see Figure 2). This pattern corresponds to a 3D situation with metal cylinders extending to infinity in both directions. • Connect the pattern to the power supply with the negative post attached to the outer circle. Using the single lead probe attached to the positive post of the DVM, measure and sketch five equipotential lines. For each of these lines measure the potential with DVM and record this data on the paper copy of your pattern geometry.

Power Supply -

+ DVM

Figure 2. Setup for measurements of electric fields in coaxial cylinders geometry. • Based on the previous experiment, predict whether the cylinders will themselves be equipotential surfaces. Make measurements to test your prediction and discuss the results. If your prediction is incorrect resolve the inconsistency between your prediction and your data. • Switch to the fixed spacing probe assembly to make measurements of the electric field between the two circles. Measure the electric field every 1cm along two different radii. Record these E values as well as the distances r from the center of circles the (choose the r value at a point exactly in the Page 3 of 4

middle of the probe tips). Represent the measured E values with little vectors on your sketch. Your measurements should start at the location of the inner cylinder. • Is the electric field perpendicular or parallel to the equipotential lines you have drawn? • Enter the measured E values and the corresponding r distances in GA. Make a plot: E vs. 1/r. The values of 1/r can be obtained using the calculated column feature (DATA → NEW CALCULATED COLUMN). To add a new graph navigate to INSERT → GRAPH and select proper axes options. • Which of the two graphs is that of a straight line? Does this mean that the electric field is directly proportional to the radius or is the electric field inversely proportional to the radius? Explain. • Measure the E-field outside the outermost cylinder. Is this result consistent with Gauss’ Law? Final conclusion: Based on your measurements state the values and properties of the electric fields for the examined configurations of electrodes. Self-assessment questions: 1. 2. 3. 4. 5. 6. 7.

Is the electric field a scalar or a vector quantity? What is the meaning of the electric field? What is the unit of the electric field? Is the electric potential a scalar or a vector quantity? What is the electric potential related to? Is the electric field uniform between two concentric circles? If the electron is moving from left to right in uniform electric field what is the direction of the field.

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