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PhyPiDAQ: Experiments on Electrostatics

Measurements of charges and with capacitors are also possible with small voltages that are harmless to pupils, if a very high-power amplifier is used with which voltage measurements can be made without disturbing current flow. For this purpose, one can use the operational amplifier A 3140 with an internal resistance >10¹² Ohm, with which an "electrometer circuit" can easily be realised and which is also included in the construction proposal for a generally applicable amplifier board.

Basics of measurement technology

The electrometer circuit is shown in Fig. 1. Since the polarity of the signal is often not clear from the outset, a symmetrical voltage supply has been foreseen so that input signals between -5V and +5V are possible. The input (1) must be connected to ground either with a resistor or with a capacitor, in order to obtain a voltage level at the input that is proportional to a small current or an electric charge.

Fig. 1: Electrometer circuit with CA3140 and balanced voltage supply ±5V with the DC-DC converter TMA0505D.
Fig. 1

If the signal is to be recorded with an analogue-to-digital converter connected to the Raspberry Pi, it is necessary to convert the output signal from ±5V to 0-5V. A simple circuit with an operational amplifier for level adjustment is shown in Fig. 2.

Fig. 2: Operational amplifier circuit for level adjustment ±5V → 0-5V.
Fig. 2

Electrostatic influence

In the following experiment, the effect of electrostatic influence will be shown. Furthermore, the same setup can also be used to demonstrate a load spoon.

An open, round capacitor plate with a diameter of d ≈ 5 cm is connected to the electrometer. The mass of the measuring case is pulled to the earth potential. A capacitor with a capacity of 1 nF is connected between the capacitor plate and the earth. The output of the electrometer is connected to the level converter and this in turn to the ADC. This means that both positive and negative voltages can be read out.

elektrostatik.daq: Fig. 3: Electrostatic experiment setup
Fig. 3

We now deal with the configuration file. For the sake of clarity, superfluous comments and lines that have been commented out have been left out.

DeviceFile: config/myADS1115Config.yaml   # 16 bit ADC, I2C bus 
ChanLabels: ['Uc']            # names for channels 
ChanUnits: ['V']         # units for channels 
ChanColors: [darkblue]      # channel colours in display
ChanFormula:
  - 2*c0-5  # chan0
Interval: 0.1                 # logging interval 
DisplayModule: DataGraphs     # text, bar-graph, history and xy-view
Title: "Data from File"       # display title

myADS1115Config.yaml:

# example of a configuration file for ADC ADS1115

DAQModule: ADS1115Config  

ADCChannels: [0]         # active ADC-Channels
DifModeChan: [false]   # enable differential mode for Channels
Gain: [1]                # programmable gain of ADC-Channel
sampleRate: 860             # programmable Sample Rate of ADS1115

You may have to adjust the Gain in the penultimate line - depending on whether the displayed signal is too small or too large. On the software side, the function of the level converter is compensated as follows:
Ucapacitor = 2 · Umeasured-5V, which is already taken into account in ChanFormula.
Before the measurement begins, the capacitor plate is connected to earth potential using a conductor so that it is uncharged. If a charged body is brought closer to the capacitor plate, the electric field of the charged body causes a force on the free electrons of the capacitor plate, which then - depending on the body's charge - are accelerated towards or away from it (electrostatic influence). This process is limited by the fact that an electric field is built up through the charge shift, which counteracts the accelerating force.

The charge separation can be measured as an electrical voltage between earth and the capacitor plate, i.e. precisely on the input side of the electrometer. It should be noted that an electrometer with a very high internal resistance is absolutely necessary for this experiment, as otherwise current flow between the input of the electrometer and the earth leads to a charge equalization on the capacitor plate and the effect is therefore not visible. The effect is not visible with a conventional multimeter. A plastic rod is used as the body, which was rubbed on a wool sweater so that it became charged. Then it is brought closer to the capacitor plate, the distance being varied several times.

Fig. 4 below shows the time course of the voltage across the capacitor. The change in voltage with the distance between the rods can be clearly seen. The sign of the voltage also shows that the rod is positively charged.

Fig. 4: Influence Time curve of the voltage on the capacitor with repeated changes in the distance to the charged rod.
Fig. 4

Charging of a capacitor with a conducting sphere

Now the demonstration of the electrical charge spoon follows. To do this, a metal ball is rubbed on a wool sweater and then the discharged capacitor plate is touched with it. The illustration shows the course of the voltage. The increase in the capacitor voltage
upon contact with the sphere indicates the charge. With Q = C · U, a known capacitance of 1 nF and the measured voltage difference of −2.7 V, the transferred charge is determined to be −2.7 nC.

Fig. 5: Electric Charge spoon Time curve of the voltage on the capacitor when approaching and touching a charged ball. At approx. 66 s the capacitor is grounded so that the voltage is 0 V. When the charged sphere approaches, the amount of voltage on the capacitor increases due to influence. When the ball touches the capacitor plate (t ≈ 67.9 s), the voltage reaches a constant value.
Fig. 5