Electric field of the atmosphere

Atmospheric Physics Lab Work

Electric field of the atmosphere

Abstract

This experiment introduces to the electric properties of the atmosphere. The absolute value of

the electric field and the vertical current is measured. The experiment is done with two metal

plates; in between a potential difference adjusts due to the terrestrial electric field. The high of

the electric field is measured with an electrometer and is then automatically recorded.

Questions to be answered during the reading of the manual (Will be discussed in a small tutorial ahead of the experiment)

Show how the diurnal cycle of the electric field looks like!

Which factors can influence the measurements?

Table of Contents

1. Introduction...4

2. Instruments and equipment...4

3. Experiment and tasks...4

3.1. Part I: The electrometer – characteristics... 5

3.1.1. Keithley electrometer - basics... 5

3.1.2. Electronic measuring equipment... 5

3.1.3. Tasks to be performed indoors... 7

3.1.3.1.Task 1:... 7

3.1.3.2.Task 2:... 8

4. Part II: Field measurements...8

4.1. Tasks...8

4.1.1.1.Task 3:... 8

4.1.1.2.Task 4:... 10

4.1.1.3.Task 5:... 10

5. Literature...12

1. Introduction

At good weather situations an electric field of about 100 V/m can be found in the lower atmosphere. The sign of the electric field strength correspond to a negative charge at the Earth’s surface. The atmosphere is not a perfect isolator. A low vertical current of about 10

A is observed. The electric conductivity of the atmosphere is caused by the ionization of the air. There is a permanent ionization equilibrium, which depends on the ratio of the built ionic pairs per unit time and volume and the reintegration coefficient. The electric field is sustained by the worldwide thunderstorm activities. There are worldwide about 40.000 thunderstorms each day. They are most frequent between 2 p.m. and 7 p.m. and they are least frequent at about 4 a.m. UTC. The electric field over the oceans and the polar regions, as well as over land shows the same diurnal circle.

2. Instruments and equipment

●

Watch with second hand (bring yourself)

●

Base plate

●

Measurement plate (diameter 800 mm with three Teflon isolators, distance 20 mm)

●

Cover plate

●

Metallic isolation box for wires

●

Keithley Electrometer (with measurement wires, output wire and BNC-Cover for Electrometer input)

●

Keep the instrument in a dry place!

●

Recorder Elviascript 3N (fix the cover with tape)

3. Experiment and tasks

Remarks: As described in the literature, electrical currents of around 10

A and electric induced charge of about 10

C have to be determined. This is only possible with very sensitive amplifiers with small input error current.

The measurements have to be done in a flat area, as elevations (buildings, mountains,…) influence the electric field. Also thunderstorms have a strong influence on the measurements;

therefore the day when the measurements take place should be free of (cumulus-) clouds.

Think about other disturbing factors.

For the realization it is necessary to get familiar with the functionality of the Keithley Electrometer. A description is given in the next paragraph. For further information consult the manual. Additionally you should know about:

•

Leveling layer, ionization of atoms and the vertical current

•

Measuring methods of air electrical parameters

•

Processes which support the conservation of the potential difference

•

Diurnal cycle of the electric field

3.1. Part I: The electrometer – characteristics

3.1.1. Keithley electrometer - basics

The basic schema to measure current and electric charge is shown in figure 3 a) and b) for the modes “normal” and “fast”, respectively. The measuring resistance and the measuring capacitor are selected with the main switch (Ampere or Coulomb). “10

” on the scale means for example that an impedance of 10

Ω or 10

F is switched into the input circuit or into the degenerative feedback circuit, depending whether the mode “normal” or “fast” is chosen. The impedance can be bypassed with the switch “lock”. In this position the error voltage U

on the amplifier input can be adjusted to zero.

The built-in meter shows the voltage of the measured impedance plus a possible error voltage.

The sensitivity of this display can be adjusted with the multiplier button (x 0.01, 0.03…10) separately. The chosen sensitivity is also transmitted to the printer output whereas polarity selection and zero offset are not transmitted to the printer output.

The attached printer has to be run with a 1 mA input signal. The output of the Keithley Electrometer (on the backside of the instrument) has to beset to 1 mA as well.

3.1.2. Electronic measuring equipment

An operational amplifier amplifies the input voltage difference (U

-U

). The output voltage U

is

U

=−v U

−U

 (1)

where v is the amplification factor.

If U

= 0 (i.e. the P-input is at the ground) then U

= -v U

. The N-Input is then called the inverted input, because a positive input signal at U

leads to a negative output signal. The real (frequent dependent) amplification factor v is very large (10

) and is considered in the following as ideal, which means infinite and frequent independent.

If a resistance or a capacitor (in general an impedance Z) is put between the inverted input and the output, then the amplifier adjusts the offset voltage U

to be 0 (Figure 2). The offset voltage U

is equal the difference of the input voltages if the output voltage U

= 0 V. In other words, the inverted input is virtually on ground. Therefore the input current is

I=U

R

. (2)

Figure 1: Operational amplifier +

- U_p

U_n

U_a

The input resistance of an operational amplifier is almost infinite. According the node rule the current I has to flow through the impedance Z. It follows

I=0−U_a Z =U

R

(3)

or solved for U

U

=−U Z

R (4)

In mode “normal” the Keithley Electrometer uses the configuration a) from Figure 3. Because the output follows the input voltage this circuit is called voltage follower. Therefore U

= 0 and also U

= U.

In mode “fast” circuit b) is realized. If the impedance Z is a capacitor with a capacity C, the input current is integrated. According to the node rule for the inverted input the total sum of the currents is

I I

= 0 . (5)

The current through the capacitor is

I

=C dU

dt . (6)

Figure 2: Determination of Ua with impedance Z

(a) “normal” mode (b) “fast” mode

Figure 3: Measurement setup for the different modes of the electrometer

+ -

Z

U

I

+ - Z

U

+ -

Z

R

U

I

Integrating this equations one obtains for U

U

=− 1

C ∫ ^{I dt . (7)}

In reality there are discrepancies from this ideal case. There are two reasons:

1. There is a small current between input and the first amplifier, called “input bias current” I

, which is integrated as well:

dU_a dt =I_B

C

(8)

2. The offset voltage at the amplifiers input is not exactly zero, due to the temperature dependency. This leads to a current through the (in reality not infinite) input impedance R

(input resistance of the amplifier parallel to the source resistance), which is integrated as well. Following

dU

dt = U

R ⋅ C = U

 (9)

With a given time constant τ, ∆U

/∆t also remains constant and the influence of I

decreases with increasing C.

3.1.3. Tasks to be performed indoors

3.1.3.1. Task 1:

The electrometer will be used as an integrator. Measurements will be done in the “fast” mode in order to have a higher sensitivity. In this way the measurements errors can be evaluated.

Parameters given:

Voltage of the current source: 2 V

Internal resistance of the current source: 2·10

Ω Isolation resistance of the measuring cable: 10

Ω

Integration time: 10 min

Leakage resistance R

of the capacitor, as

well as the time constant of the entity

(C·R

): 10

s Isolation resistance of the switch: 10

Ω

Offset voltage: 1 mV

The circuitry can be reset before every measurement such that U

= 0 V. The offset voltage can vary due to the influence of temperature fluctuations. For determining the average of the measured current, the short-circuit current can be used. The amplification factor can assumed to be infinity.

1

Time when the charge of the capacitor drops down at 1/e of the charge exit.

The equivalent circuit diagram (with all leakage- and isolation resistances) for the “fast” mode is shown. Now the errors considering the values given above have to be determined. Choose the best capacitor using the appropriate switch. The results have to be discussed and compared with a bias current of the amplifier input I

< 10

A.

3.1.3.2. Task 2:

The drift of U

, the current error, as well as the input resistance R

must be determined.

The Keithley Electrometer will be used and the batteries must be controlled (check out the manual).

1. Drift of U

: Settings: tuning “fast”, “Coulomb” (different values), position “lock”.

2. Bias current I

: Settings: tuning “fast”, 10

C, position “unlock” (at the beginning still on

“lock”). Lock the input with the BNC-closing cap (protection against outer fields). Set the zero-check switch on “unlock” (the capacitor begins to load) and change the charge to a time scale of about 15 min. The expecting current is increasing to about 10

A.

3. Input resistance R

: Settings: tuning “fast”, 10

C, position “unlock” (at the beginning still on “lock”). Set the offset U

as high as possible (in the chosen multiplication domain) and measure again the bias current. To determine the error current caused by charges in the isolation: Repeat the measurements with the input cable attached to the instrument while the ends are isolated from the metal holders (do not allow the cables to be in contact with each other or other metal pieces). Disturbances through charged isolators can be determined by setting the offset positively and then negatively.

4. Part II: Field measurements

4.1. Tasks

4.1.1.1. Task 3:

Determination of the vertical current, as well as the intensity of the electric field. On a plain location, the electrometer is attached to the base plate and the measurement plate (Fig. 4). The recorder (scale 1 mA) is connected to the Keithley electrometer and their indicators must be in accordance with each other. Before connecting the cables for the measurements, both plates have to be short-circuited.

Figure 4: measurement scheme

Electrometer settings: tuning “fast”, 10

C, position “lock”.

The measurement pate is now covered with a shield pate without touching it (phase 1, see fig.

5). The shield plate is linked with the base plate (same potential). After switching the electrometer to “unlock” and removing the shield plate, the electrometer should indicate a voltage of about 1 V. (phase 2, see fig. 6). The measurement reacts to static charges on clothes, so be as far as possible from the measurement location. After about 15 min, the shield plate has to be placed carefully in its initial position. The measured value is then noted after approximately 1 min. It corresponds to the vertical current flux (phase 3, see fig. 5).

Figure 5: phase 1 and phase 3

The electrometer should be set back to zero with “lock”. The cycle must then be repeated.

Now the vertical current and the electric field are measured during 3 hours regarding the description made above. The results should be presented graphically and the weather should be characterized.

a. without attached electrometer

b. with electrometer Figure 6: phase 2

Note: During phase 1 (covered measurement plate) the charges that are induced on the

measurement plate by the terrestrial field are supplied by integration capacitor. Since the

electronics draw the measurement plate to zero potential, the induced charges can be directly

read in Coulomb. Now consider the measurement plate with a surface F. As a first

approximation, the plate is assumed to be at zero elevation. Now the electrical field can be calculated with the measured charge Q as:

E=Q

F

(10)

This formula is valid only for the setting “fast” (Why?).

Note: The induced charge is bigger by a form factor f compared with the value obtained by equation (10) because the measurement plate is elevated by the distance between the plates and thus not at zero elevation.

During phase 2 (15 min with open measurement plate), the integration is done with the same capacity to measure the vertical current. While for the discussion of phase 1 was the model of induced charges was used, phase 2 can be better explained by assuming that the two plates form a capacitor where the enclosed air acts as an electrolyte.

In phase 3 (covered measurement plate) a voltage drop occurs through the induced charges during phase 2. This drop doesn’t need to be as high as the one in phase 1, since the terrestrial field might have changed in the meantime. Please try to imagine what happens within the attached electronics during the 3 phases.

4.1.1.2. Task 4:

Record the current for 15 min. with a covered measurement plate for U

= 0, U

= max and U

= min. Discuss the results especially considering the surface potential. Electrometer settings:

mode “fast”, 10

C, position “lock”.

4.1.1.3. Task 5:

Estimate the form factor f. The electric field of the capacitor expands into the surrounding at the edges of the plates. As a result, the induced charge as well as the electric field will be bigger than calculated.

Figure 7: form factor f. Interaction between the terrestrial field and the capacitor field

Determine the open-circuit voltage of the measurement plate that is the voltage of the plate at

an elevation h without any charges. Now determine the charge that is needed to bring the

measurement plate to ground potential. In the calculations the capacity of the measurement

plate can be split into two terms: the capacity of the plate and the stray capacitance (edge

effects and surface capacity). The stray capacitance has to be guessed or can be derived from

measurements of the total capacity. To determine the form factor f of the vertical current

consider the analogy between the charge that is induced by the electric field and the current

that is caused by the conductivity of the air.

5. Literature

[1] Gösta H. Liljequist, Konrad Cehak (1984): Allgemeine Meteorologie. Vieweg, 179-199.

[2] Richard P. Feynman, Robert B. Leighton, Matthew Sands (1987): Feynman Vorlesungen über Physik Band II. Oldenbourg, 166-182.

[3] H. Israel (1961): Atmosphärische Elektrizität Teil II. AVG, Paragraph 56-58, 78-89.

[4] Ulrich Tietze, Christoph Schenk (1985): Halbleiterschaltungstechnik. Springer Verlag, Paragraph 7.

[5] Manual Keithley Elektrometer, and Schreiber Elviascript.