2
Electric field in a plate capacitor
Objectives:
The purpose of this experiment is to:
·
Measure the electric field within a plate capacitor as a function of the distance between the
plates.
·
Measure the electric field within a plate capacitor as a function of the applied
voltage. Apparatus:
The experiment requires a DC power supply 500 V, Resistor 300 k , contact rod, digital Multimeter,
Electric Field Meter (see Fig.1), 1 mm Plexiglas spacer discs.
1
2
7
3
8
4
5
6
9
10
1
2
3
4
5
6
7
8
9
Shielding plate
Screening cylinder
Earth socket
Output voltage socket
Earth socket for output
Mains switch
Measurement range switch
Offset adjustment
Voltage measurement
plate
for 1×range
plate
10..Voltage measurement
for 10×range
2
11 Capacitor plate, 250 cm
12 Plexiglas spacer discs
13..Capacitor plate for voltage
2
measurements, 250 cm
11
12
13
Fig. 1. Electric Field Meter
Basic principles
The electric field meter can be used to measure electric fields directly. In front of an induction plate with
four sectors in a star-shaped arrangement, a fan-like disc of similar shape is rotated (see Fig.2). It
continually interrupts the electrostatic flux, and thereby causes periodic induced charges, which are allowed
to dissipate through a large resistance. The voltage pulses that are thereby generated are
University of Boumerdes, Institute of Electrical and Electronic Engineering, EE-178L (Physics II)
Page 1
amplified to give an output voltage, which is then rectified to give a DC voltage that is proportional to
the electric field E acting on the induction plate.
In the experiment, the electric field strength is given by:
E
U
…………………(1)
d
In a plate capacitor is measured using the electric field meter. The applied voltage U and the distance d
between the plates are varied in separate experimental runs.
In applying Equation (1), one must take into account the fact that the induction plate is about 1 mm
below the lower capacitor plate. Therefore, Equation (1) must be replaced by:
E
U
d eff
U
…………………(2)
d 1(mm)
Fig. 2. Rotating disc of electric field meter.
Procedure:
Zero-point calibration
·
Set up the experiment as shown in Fig. 3.
·
Connect the digital multimeter to the voltage output of the electric field meter.
·
Place the voltage measurement plate in position at the shorter distance and secure it with the
knurled screw.
·
Turn the measurement range switch to the “U” position and set to the highest range.
·
Connect the measurement plate to the earth socket of the screening cylinder.
·
Switch on the electric field meter and set the zero point using offset adjustment.
·
Calibrate the zero-point for the two lower measurement ranges by the same procedure.
Vv
E
U
Fig. 3: Calibration set-up
University of Boumerdes, Institute of Electrical and Electronic Engineering, EE-178L (Physics II)
Page 2
Part I: Measurement of the Electric field as a function of plate separation
·
Set up the experiment as shown in Fig. 4.
·
Place the capacitor plate for voltage measurements on the screening cylinder and secure it
with the knurled screw.
·
Place the required spacer discs on the capacitor plate for voltage measurements and then
adjust plate separation to d = 1 mm (deff = 2 mm) by placing the three 1 mm spacer discs
about 120° apart on the edge of the capacitor plate for voltage measurements.
·
Put the capacitor plate on top of them.
·
Turn on the DC power supply and set the voltage to U = 200 V.
·
For all measurements, hold the contact rod it in your hand, so that you are also at the same
potential.
·
Select a measuring range of 300 V/cm on the electric field meter. This range will be
multiplied to the read value.
A voltage of 1 V read off from the analogue multimeter corresponds to an electric field of 300 V/cm .
·
Enter the voltage reading from the digital multimeter as the value of the electric field in units
of V/m into Table 1.
·
Turn off the electric field meter and discharge the capacitor plate by touching the top plate
with the contact rod.
·
Repeat the measurement with the same applied voltage U= 200 V for plate separations of d =
2, 3, 4, 5, 6 and 7 mm (Table 1) and enter the field strengths you measure next to the
corresponding effective separations deff in Table 1.
·
Repeat the experiment three more times.
Fig. 4: Measurement set-up
University of Boumerdes, Institute of Electrical and Electronic Engineering, EE-178L (Physics II)
Page 3
Part II: Electric field as a function of applied voltage
·
Keep the same setup as shown in part I
·
Set the plate separation to d = 4 mm (deff = 5 mm).
·
Turn on the DC power supply and set the voltage to U = 50 V.
·
Select a measuring range of 300 V/cm on the electric field meter.
A voltage of 1 V read off from the digital multimeter corresponds to an electric field of 300 V/cm.
·
Enter the voltage reading from the digital multimeter as the value of the electric field in units
of V/m into Table 2.
·
Turn off the electric field meter and discharge the capacitor plate by using the contact rod.
·
Repeat the measurement with the same plate separation d = 4 mm for voltages of U = 100,
150, 200, 250, 300, 400 and 500 V and enter the field strengths you measure next to the
corresponding voltages in Table 2.
·
Repeat the experiment three more times.
Analysis
Part I:
·
Plot the measured electric field strengths E against the effective plate separations deff for the
fixed applied voltage U=200 V.
·
For each value of the thickness deff, compute the product E deff. What should the value of this
product have been?
·
To get the right result we should multiply the product E deff by a constant . Determine the
value of this constant.
·
Do you think that really 1V corresponds to 300V/cm? if not so what should be the right
correspondence?
Part II:
·
Plot the measured electric field strengths E against the applied voltage U for the fixed
effective plate separations deff =5 mm.
·
Determine the experimental dependence of E against the applied voltage U.
·
What is going to be the dependence of E against the applied voltage U if we apply the
correspondence you found in the last question of the part I? Compare your result with the
theoretical expectation.
University of Boumerdes, Institute of Electrical and Electronic Engineering, EE-178L (Physics II)
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Data Collection for part I:
Tab. 1: Electric field strength as a function of plate separation for U = 200 V.
deff (mm) 2
E1(V/cm)
E2(V/cm)
E3(V/cm)
Eav(V/cm)
3
4
5
6
7
8
Data Collection for part II:
Tab. 3: Electric field strength as a function of applied voltage U for d = 4 mm.
U (V) 50
E1(V/cm)
E2(V/cm)
E3(V/cm)
Eav(V/cm)
100
150
200
250
300
400
University of Boumerdes, Institute of Electrical and Electronic Engineering, EE-178L (Physics II)
500
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