Following the motion of a charged conducting sphere by electrostatic induction in a parallel plate capacitor

doi:10.1016/j.elstat.2019.103411

Journal of Electrostatics

Volume 103, January 2020, 103411

https://doi.org/10.1016/j.elstat.2019.103411 Get rights and content

Highlights

•
Electrostatic induction in a parallel plate capacitor induced by charged sphere.
•
Linear distance dependence of the induced charge for distances larger than the radius.
•
Motion of the charge on the conducting sphere for closer distance.
•
An approximate formula for the induced charge in comparison to experimental results.

Abstract

The charges induced in the plates of a parallel plate capacitor due to a conducting charged moving sphere have been measured up to the mechanical contact. For larger distances the induced charge scales linearly with the distance. However, when the sphere approaches the plate further the charges on the sphere are attracted by the induced charges in the plate and move on the surface of the sphere towards the plate. This leads to a further increase of the induced charge. The experimental results compare well to an approximate formula which will be discussed in detail.

Introduction

There are several non intruding methods to trace the motion of a small object. E.g. various schemes of optical detection are widely used. However, if the experiment is confined to a non transparent housing other techniques are required. This may be achieved by monitoring induced charges if the object to be studied carries an electrostatic charge. The current generated by a transient image charge has been described for a particle moving in the vicinity of an electrode [1,2]. Different arrangements of electrodes are conceivable, e.g. tubes [3,4], parallel plate capacitors or a coaxial set of three electrodes [5]. Amongst others experiments were performed e.g. for projectiles with high speed [[6], [7], [8]].

Recently, we have shown that using electrostatic detection it is possible to follow the motion of a weakly charged object in all three dimensions with an excellent temporal resolution which exceeds the one of conventional high speed cameras [9]. The detection relies on the charge induced in an electrode which can be measured by a charge sensitive amplifier. In many cases a satisfactory agreement between the real trajectory and the one deduced from the measured charge is obtained assuming a point charge instead of an extended charge distribution. In the present paper we will consider in detail, how the induced charges vary with distance when a conducting sphere comes close to the surface of the electrode. As will be shown an almost accurate description can be given for distances down to less than a hundredth of the radius of the sphere.

Section snippets

Principle of the experiment

Fig. 1 displays the basic scheme of the experiment. The detection of the motion and of the charge of the sphere are based on electrostatic induction. The sphere is falling through a small hole (not shown in the sketch) into a parallel plate capacitor. The lower plate is grounded by connecting it to a very sensitive charge amplifier. The charge of the sphere induces image charges on the upper and lower plate of the capacitor, both of opposite sign. If one assumes a point charge instead of the

Method

For the presented study it is important to know the trajectory and the charge of the sphere. To obtain a well defined motion in the vertical direction, the free fall of a sphere is studied. $z = - \frac{1}{2} g {(t - t_{0})}^{2} + v_{0} (t - t_{0}) + z_{0}$ where g is the gravitional acceleration, $v_{0}$ and $z_{0}$ are the initial conditions for the velocity and the height at $t_{0}$ . If the sphere bounces from a horizontal plate, $v_{0}$ and $z_{0}$ may be easily determined for each section. If $t_{1}$ and $t_{2}$ are the successive times when the sphere touches the

Results

The lower part of Fig. 3 displays the measured charge on the lower plate of the capacitor while a stainless steel sphere is bouncing on the lower plate. The full dataset including simulations using formulas (1) and (4) is available in Ref. [14]. The moments of mechanical contact, indicated by the vertical dashed lines, are clearly visible. The data are slightly complicated because the charge of the sphere changes at each contact to the plate. Due to the conservation of charge, the charge

Summary

The induced charges in a parallel plate capacitor may be used to accurately determine the position of a charged sphere in the direction normal to the plates. However, when the sphere approaches one of the plates the motion of the charge on the surface of the sphere has to be considered. Based on known formulas for the mutual capacitance between a sphere and a plate a formula is given which provides an accurate description of the induced charge. The comparison to the data measured for a charged

Declaration of competing interest

The authors declare that there is no conflict of interest.

Acknowledgement

The work was funded by the Elstatik Foundation, Germany (Project No.: 440701010750005).

References (14)

J. Peltonen et al.
Sens. Actuators A Phys.
(2016)
S. Banerjee et al.
IEEE Trans. Ind. Appl.
(2017)
W. Shockley
J. Appl. Phys.
(1938)
S. Ramo
Proceedings of the IRE
(1939)
M. Gamero-Castano
Rev. Sci. Instrum.
(2007)
B.L. Barney et al.
Rev. Sci. Instrum.
(2013)
J. E. Nanevicz and W. C. Wadsworth, 32...

There are more references available in the full text version of this article.

Cited by (7)

Cosmic radiation does not prevent collisional charging in (pre)-planetary atmospheres
2021, Icarus
Citation Excerpt :
The spheres falling through the copper rings electrically induce a voltage depending on the charge, which is amplified by the LAMA. This charge detector is a recent development (Genc et al., 2019; Kaponig et al., 2020). The output of the LAMA is fed to a 16 bit AD-converter and charges (voltages) are measured 860 times per second.
In (pre)-planetary environments, dust and sand grains regularly collide. They electrically charge and discharge during these events. In this work, we study if cosmic radiation has any influence on the equilibrium charge state on timescales of minutes. We developed an experiment that was carried out during the ascent of a stratospheric balloon. With increasing altitude, the radiation activity increases by a factor of 54. However, we found only a very minor decrease in grain charges of up to 30%. This implies that charge-moderated processes from thunderstorms on Earth, over early phases of planet formation to particle motion on the Martian surface on short timescales essentially proceed unhindered from a direct influence of cosmic radiation.
Single-Electron-Precise Tailoring of a Resistive-Switching Device by Tuning Transfer Printing Parameters: A Computational Study
2023, IEEE Transactions on Electron Devices
Dynamics of contact electrification
2021, Science Advances
A smoking gun for planetesimal formation: Charge-driven growth into a new size range
2021, Astrophysical Journal Letters
A smoking gun for planetesimal formation: Charge driven growth into a new size range
2021, arXiv
Dust Concentration Detection Technology Based on Fusion of Light Scattering Method and Charge Induction Method
2021, Dongbei Daxue Xuebao/Journal of Northeastern University

View all citing articles on Scopus

View full text

Short communicationFollowing the motion of a charged conducting sphere by electrostatic induction in a parallel plate capacitor

Highlights

Abstract

Introduction

Section snippets

Principle of the experiment

Method

Results

Summary

Declaration of competing interest

Acknowledgement

Sens. Actuators A Phys.

IEEE Trans. Ind. Appl.

J. Appl. Phys.

Proceedings of the IRE

Rev. Sci. Instrum.

Rev. Sci. Instrum.

Short communication
Following the motion of a charged conducting sphere by electrostatic induction in a parallel plate capacitor