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^{1}, M. Shen

^{1}, J. Xu

^{1}, W. X. Chen

^{1}, Y. Jin

^{1}, W. N. Peng

^{1}, X. B. Fu

^{1}and L. W. Zhou

^{1,a)}

### Abstract

A local electric field distribution in the midplane between two spherical metal particles under an applied electric field is measured for comparison with the real electrorheological system. It was found that the ratio of the maximum value of local electric field to applied electric field is not a constant as most theoretical models predicted.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 1024402 and 10334020) and the Tang Zhongying Science Creative Foundation (B2 807).

### Key Topics

- Electric fields
- 33.0
- Electric measurements
- 4.0
- Electrodes
- 4.0
- Kerr effects
- 4.0
- Polarization
- 4.0

## Figures

The measured light intensity and a schematic diagram of the arrangement of the spheres in the experiment. The applied electric field is . There are four balls arranged in a line, and the radius of each ball is while the distance between two neighboring balls is . In the insets, the origin point is defined as the midpoint of the line segment joining the centers of the two neighboring spheres; the axis is defined as the direction of , and the axis is defined to be perpendicular to in the paper plane. The light propagates along the axis.

The measured light intensity and a schematic diagram of the arrangement of the spheres in the experiment. The applied electric field is . There are four balls arranged in a line, and the radius of each ball is while the distance between two neighboring balls is . In the insets, the origin point is defined as the midpoint of the line segment joining the centers of the two neighboring spheres; the axis is defined as the direction of , and the axis is defined to be perpendicular to in the paper plane. The light propagates along the axis.

The distribution of the local electric field along the axis in Fig. 1. Line 1 indicates the result when , line 2 indicates the result when , and line 3 indicates the result when . In plot (a), there are two spheres both in radius, and the shortest distance between the neighboring spheres is . In plot (b), there are four spheres with the same radius as that in plot (a), and arranged in a line with the same shortest distance as in plot (a). If the applied field is higher than , the signal of light intensity is not stable.

The distribution of the local electric field along the axis in Fig. 1. Line 1 indicates the result when , line 2 indicates the result when , and line 3 indicates the result when . In plot (a), there are two spheres both in radius, and the shortest distance between the neighboring spheres is . In plot (b), there are four spheres with the same radius as that in plot (a), and arranged in a line with the same shortest distance as in plot (a). If the applied field is higher than , the signal of light intensity is not stable.

The ratio vs . The dash-dot-dotted line is the theoretical prediction of based on the conduction model considering the many-body effect and the equipotential assumption. The dotted line is the highest ratio of that can be deduced from the point dipole model (Ref. 3). The dashed and solid lines are our experimental results of two-sphere and four-sphere cases, respectively. The dash-dotted and the short-dashed lines are the simulation results of two-sphere and four-sphere cases, respectively.

The ratio vs . The dash-dot-dotted line is the theoretical prediction of based on the conduction model considering the many-body effect and the equipotential assumption. The dotted line is the highest ratio of that can be deduced from the point dipole model (Ref. 3). The dashed and solid lines are our experimental results of two-sphere and four-sphere cases, respectively. The dash-dotted and the short-dashed lines are the simulation results of two-sphere and four-sphere cases, respectively.

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