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Measurement of electric fields and estimation of dielectric susceptibility
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10.1119/1.4793439
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Affiliations:
1 College of Science and Technology, Nihon University, Tokyo 101-8308, Japan
2 College of Industrial Technology, Nihon University, Chiba 275-8576, Japan
a) Electronic mail: ya.nogi@nifty.com
Am. J. Phys. 81, 359 (2013)
/content/aapt/journal/ajp/81/5/10.1119/1.4793439

### References

• Yasuyuki Nogi, Kiyomitsu Suzuki and Yasunori Ohkuma
• Source: Am. J. Phys. 81, 359 ( 2013 );
1.
1. M. Misakian, F. R. Kotter, and R. L. Kahter, “ Miniature ELF electric field probe,” Rev. Sci. Instrum. 49(7 ), 933935 (1978).
http://dx.doi.org/10.1063/1.1135497
2.
2. B. R. Thomas, “ Quantitative electric field measurements in an intermediate laboratory,” Am. J. Phys. 74(4 ), 255259 (2006).
3.
3. J. P. Donohoe, “ A laboratory experiment to demonstrate Gauss's law for electric fields,” Am. J. Phys. 76(10 ), 963967 (2008).
http://dx.doi.org/10.1119/1.2952441
4.
4. M. P. Dinca, “ Charge sniffer for electrostatics demonstrations,” Am. J. Phys. 79(2), 217221 (2011).
http://dx.doi.org/10.1119/1.3531961
5.
5. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon Press, Oxford, 1984), p. 199.
6.
6. Y. Ohkuma, T. Ikeyama, and Y. Nogi, “ Double-sensor method for detection of oscillating electric field,” Rev. Sci. Instrum. 82(4 ), 0435011 (2011).
http://dx.doi.org/10.1063/1.3571299
7.
7.See Ref. 5, p. 25.
8.
8. M. DiStasio and W. C. McHarris, “ Electrostatic problem? Relax!Am. J. Phys. 47(5 ), 440444 (1979).
http://dx.doi.org/10.1119/1.11802
9.
9.See Ref. 5, p. 34.
10.
10.See Ref. 5, p. 18.
http://aip.metastore.ingenta.com/content/aapt/journal/ajp/81/5/10.1119/1.4793439
View: Figures

## Figures

Fig. 1.

Disk-type EF sensor consisting of conducting plates and guard rings. Charges induced on the conducting plates flow through resistor . Voltage signals across are observed using an oscilloscope.

Fig. 2.

(Color online) Top view of EF sensor. The conducting plate is electrically isolated from the guard ring (painted in black) using a thin plastic film. The signal cables between the conducting plates and terminals A and B are covered with an electrostatic shield.

Fig. 3.

Experimental setup. A potential with and  = 300 kHz is supplied between the p-electrode and n-electrode. Nodes C and D in the resistive voltage divider are used to measure . Nodes E and F are used to measure the charge on the p-electrode.

Fig. 4.

Reciprocal distance dependence of the electric field in a parallel-plate capacitor. Closed circles and triangles are electric fields measured by EF sensors with and without guard rings, respectively. The solid line denotes the electric field computed from the potential of the electrodes.

Fig. 5.

Distance dependence of the electric field, normalized by its value at  = 0 on the central plane of a parallel-plate capacitor with  = 4 cm. The radius of the electrode is marked, and the horizontal line at  = 8 cm denotes the diameter of the conducting plate in the EF sensor. The solid line denotes the electric field computed from the potential of the electrodes.

Fig. 6.

Pair of strip electrodes used for generating linear charge distributions parallel to the -axis. The rectangular-type EF sensor is installed at the origin along the -axis to detect the -component of the electric field.

Fig. 7.

Reciprocal distance dependence of the electric field divided by the linear charge density of the p-electrode. Closed circles are obtained from the measured values and λ. The solid and dashed lines are calculated from Eqs. , respectively.

Fig. 8.

Pair of small disk electrodes with surface charge densities . A disk-type EF sensor installed between the electrodes detects the -component of the electric field.

Fig. 9.

Electric field produced by small disk electrodes. The abscissa denotes the reciprocal square distance and the ordinate denotes the electric field divided by the charge on the p-electrode. Closed circles denote measured values. The solid and dashed lines are calculated from Eqs. , respectively.

Fig. 10.

Two sets of long double-plate electrodes at , parallel with the -axis, that are used for generating continuous linear distributions of dipole moments. The distance between the p-electrode and n-electrode is δ. A rectangular-type EF sensor for measuring is installed along the -axis.

Fig. 11.

Sectional drawing of electrodes and EF sensors on the -plane at . The electrodes are rotated in the clockwise direction to measure the θ dependence of the electric field. We define on the -axis. The surfaces of the EF sensor are oriented to the -axis to obtain and to the -axis to obtain . Shaded areas between the electrodes denote the dielectric samples used in Sec. .

Fig. 12.

Distance dependences of electric fields produced by continuous linear distributions of dipole moments. The ordinate is the electric field divided by the charge on the p-electrode. Closed triangles and circles denote measured values of and , respectively. Solid lines are calculated from the right-hand side of Eq. divided by for at and from Eq. for at .

Fig. 13.

Azimuthal dependences of electric fields produced by continuous linear distributions of dipole moments. Closed triangles and circles denote measured values of and at , respectively. Solid lines are calculated from Eqs. .

Fig. 14.

Linear relation between dielectric polarization and electric field . The dielectric samples are (a) neoprene rubber, (b) cushion rubber, (c) bakelite, and (d) acryl glass. Solid lines are fitting lines of data for each sample.

Fig. 15.

Dielectric susceptibility χ as a function of specific permittivity . Labels (a) through (d) refer to the samples in Fig. . The solid line denotes the theoretical relation .

/content/aapt/journal/ajp/81/5/10.1119/1.4793439
2013-04-16
2014-03-10

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