Experiment# 2

Dielectric Constant of Different Materials

Introduction:
The dielectric constant ε is determined by measuring the charge of a plate capacitor to which a
voltage is applied in both the air and presence of dielectric material (plastic) between the plates. In
this experiment, the dependence of the electrostatic induction charge from voltage, with and without
plastic sheet (without air gap) is examined in the space between the plates with the same distance
between the plates. The ratio between the electrostatic induction charges allows to determine the
dielectric constant ε of plastic.

Keywords:
Maxwell’s equations, Electric constant, Capacitance of a plate capacitor, Real charges, Free
charges, Dielectric displacement, Dielectric polarization, Dielectric constant.
Conceptual Objective:
1. To establish the relation between charge Q and voltage UC using a parallel plate capacitor
separated by air gap.
2. To establish the relation between charge Q and voltage UC using a plate capacitor with different
dielectric materials and to determine dielectric constants of different materials.
Questions to be prepared before coming to the lab:
1. What do you mean by Dielectric Constant?
2. What happens when a Dielectric is inserted into a Capacitor?
3. Why are Dielectrics used in Capacitor?

Theory and Evaluation:

Electrostatic processes in vacuum are described by the following integral form of Maxwell’s
equations:
𝑸
⃗ 𝒅𝑨
∯𝑬 ⃗⃗ = (1)
𝜺 𝒐

∮ ⃗𝑬 ⃗ =𝟎
⃗ 𝒅𝑺 (2)
Where E is the electric field intensity, Q is the charge enclosed by the closed surface A, εo is the
electric permittivity constant and S is a closed path.
If a voltage Uc is applied between two capacitor plates, an electric field E will prevail between the
plates, this is defined by:
𝟐
⃗ 𝒅𝒓
𝑼𝒄 = ∫ 𝑬 ⃗
𝟏

Due to the electric field, electrostatic charges of the opposite sign are drawn towards the surfaces of
the capacitor and voltage sources do not generate charges, but only can separate them, the absolute
values of the opposite electrostatic induction charges must be equal. Assuming the field lines of the
electric field always to be perpendicular to the capacitor surfaces of surface A, due to symmetry,
which can be experimentally verified for small distances d between the capacitor plates, one obtains
from equation (1):
𝑸 𝟏
= 𝑬 . 𝑨 = 𝑼𝑪 × 𝑨 × (3)
𝜺𝒐 𝒅

The volume indicated in Fig. 6, which only encloses one capacitor plate, was taken as volume of
integration. As the surface within the capacitor may be displaced without changing the flux, the
capacitor field is homogeneous. Both the flow and the electric field E outside the capacitor are zero,
because for arbitrary volumes which enclose both capacitor plates, the total enclosed charge is zero.
The charge Q of the capacitor is thus proportional to voltage; the proportionality constant C is
called the capacitance of the capacitor.
𝑨
𝑸 = 𝑪𝑼𝑪 = 𝜺𝒐 𝒅 . 𝑼𝑪 (4)

The linear relation between charge Q and voltage U applied to the otherwise unchanged capacitor is
represented in Fig. 3. Equation (4) further shows that the capacitance C of the capacitor is inversely
proportional to the distance d between the plates:
𝟏
𝑪 = 𝜺𝒐 𝑨. 𝒅 (5)

For constant voltage, the inverse distance between the plates, and thus the capacitance, are a
measure for the amount of charge a capacitor can take.
Figure 2: Generation of free charges in a dielectric through polarization of the molecules in the electric
field of a parallel plate capacitor.

Things change once insulating material (dielectrics) is inserted between the plates. Dielectrics have
no free moving charge carriers, as metals have, but they do have positive nuclei and negative
electrons. These may be arranged along the lines of an electric field. Formerly non-polar molecules
thus behave as locally stationary dipoles. As can be seen in Fig. 2, the effects of the single dipoles
cancel each other macroscopically inside the dielectric. However, no partners with opposite charges
are present on the surfaces; these thus have a stationary charge called a free charge.
The free charges in turn weaken the electric field of the real charges Q, which are on the capacitor
plates, within the dielectric.
The weakening of the electric field within the dielectric is expressed by the dimensionless, material
specific dielectric constant ε (ε = 1 in vacuum):
⃗
⃗⃗ = 𝑬𝒐
𝑬 (6)
𝜺

Where Eo is the Electric field generated only by the real charges Q. Thus, the opposite field
generated by the free charges must be;
⃗⃗ 𝒇 = 𝑬
𝑬 ⃗⃗ = 𝝐 − 𝟏 𝑬
⃗ 𝒐−𝑬 ⃗⃗ 𝒐 (7)
𝝐

Neglecting the charges within the volume of the dielectric macroscopically, the free surface charges
(± Qf) generate effectively the opposite field:
𝑸 𝑸𝒇 . 𝟏 𝒑
⃗⃗⃗⃗
𝑬𝒇 = 𝑨𝜺𝒇 = 𝑽𝜺 = 𝜺𝒐 𝑽 (8)
𝒐 𝒐
Where p is the total dipole moment of the surface charges. In the general case of an inhomogeneous
dielectric, equation (8) becomes:
⃗⃗
⃗𝒇= 𝟏
⃗𝑬 𝒅𝑷 𝟏
= 𝜺 ⃗𝑷
⃗ (9)
𝜺 𝒐 𝒅𝑽 𝒐

Where P is the total dipole moment per unit volume. It is called Dielectric Polarization. If
additionally, a D field is defined;
⃗𝑫
⃗⃗ = 𝜺 . 𝜺𝒐 . ⃗𝑬
⃗ (10)
Whose field lines only begin or end in real (directly measurable) charges, the three electric
magnitudes, field intensity, Dielectric displacement and Dielectric polarization are related to one
another through the following equation;
⃗𝑫
⃗⃗ = 𝜺𝒐 . ⃗𝑬
⃗ + ⃗𝑷
⃗ = 𝜺 . 𝜺𝒐 . ⃗𝑬
⃗

Figure 3: Electrostatic charge Q of a plate capacitor as a function of the applied voltage UC

If the real charge Q remains on the capacitor, whilst a dielectric is inserted between the plates,
according to definition (3), voltage Uc between the plates is reduced as compared to voltage Uvac in
vacuum (or to a good approximation, in air) by the dielectric constant:
𝑼𝒗𝒂𝒄
𝑼𝑪 = (11)
𝜺

Similarly, one obtains from the definition of capacitance (4):

𝑪 = 𝜺 . 𝑪𝒗𝒂𝒄 (12)
The general form of equation (4) is thus:
𝑨
𝑸 = 𝜺 . 𝜺𝒐 . . 𝑼𝑪 (13)
𝒅

In Fig. 3, charge Q on the capacitor is plotted against the applied plate voltage UC for comparison to
the situation with and without plastic plate between the capacitor plates, all other conditions
remaining unchanged: thus, for the same voltage, the amount of charge of the capacitor is
significantly increased by the dielectric, in this example by a factor of 2.9.
If the charges obtained with and without plastic (equations (4) and (13)) are divided by each other;
𝑸𝒑𝒍𝒂𝒔𝒕𝒊𝒄
=𝜺 (14)
𝑸𝒗𝒂𝒄𝒖𝒖𝒎

The obtained numerical value is the dielectric constant of the plastic.

In order to take into consideration, the above described influence of free charges, Maxwell’s
equation (1) is generally completed by the dielectric constant ε of the dielectric which fills the
corresponding volume:

∯𝑨 𝜺. 𝜺𝒐 ⃗⃗⃗⃗
. 𝑬𝒅𝑨⃗⃗ = ∯ 𝑫
⃗⃗ 𝒅𝑨
⃗⃗ = 𝑸 (15)
Thus, equation (13) becomes equation (4).

Experiment:
Equipment:
Voltmeter, Plate capacitor, Plastic sheet, Connecting cord, Adapter, Screened cable and Capacitor.
Setup:
The experimental setup is shown in Fig. 1 and the corresponding wiring diagram in Fig. 4. The
highly insulated capacitor plate is connected to the upper connector of the high voltage power
supply over the 10 MΩ protective resistor which limits the maximum output current to 0.5 mA.
Both the middle connector of the high voltage power supply and the charge stored on the opposite
capacitor plate is transferred to a known capacitor Cref (220nF). Then, voltage across Cref is fed to an
electrometer amplifier and the electrostatic induction charge on the parallel plate capacitor can be
measured over the digital multi-meter (DMM) voltage (UDMM) on the 220 nF capacitor, according to
equation (4). Correct measurement of the initial voltage (UDMM) on digital multi-meter is to be
assured by the corresponding adjustment of the toggle switch (discharge key) on the measuring
amplifier. The measuring amplifier (see in Fig. 5) is set to high input resistance, to amplification
factor 1 (100) and to time constant 0.
 Figure 4: Wiring Diagram

Procedure:
1. To start with, the surface of the capacitor plates is determined by means of their radius.
2. For this experiment, we will be needing 0-5kV from the power supply (see in Fig. 5). So select
the range of the power supply accordingly. The middle terminal will act as “0” for 0 – 5kV range
(see in Fig. 5). Please switch off the supply when not in use and be extremely careful while
handling this high voltage source.

3. For charging the capacitor plates, connect the highly insulated capacitor plate connected to the
positive terminal of the high voltage power supply through the 10 MΩ protective resistor which
limits the maximum output current to 0.5 mA. The other plate is connected to the middle terminal of
the power supply and grounded (see in Fig. 4).
4. Similarly, for discharging the parallel plate capacitor, remove the high voltage probe and switch
off the power supply. Connect the BNC cable to the insulated plate. The other end of the BNC is
connected to the 220nF reference capacitor (Cref) through a T-connector.
5. The voltage appearing across 220nF reference capacitor (Cref) is fed to the amplifier and the
output of the amplifier is read out on a digital multi-meter (press DC button and set its voltage knob
at 20V). The amplifier (see in Fig. 5) should be set to: i) high input resistance, ii) amplification
factor at 1 (100) and iii) time constant at 0.
Caution: Be sure not to be near the capacitor during measurements, as otherwise the electric
field of the capacitor might be distorted.
For Air gap:
6. Set the air gap between the two plates to be around 10 mm using the Vernier attached to the
capacitor plate.
7. Check that output voltage on digital multi-meter which should be 0 by doing “zero adjustment”
(to be done once just at the beginning of the experiment) and then using “reset to zero” button (to
ensure the Cref is completely discharged) before taking every measurement.
8. Set the voltage (UC) on the power supply at 0.5kV.
9. Charge the capacitor plate for 15-30 seconds. Once charged completely, remove the high voltage
probe and switch off the power supply.
10. Just insert the screening probe (or the adapter connected to the BNC test cable on the amplifier)
in the same charging capacitor plate only for 1 sec (follow steps 3 and 4) and immediately take it
out. Caution: Do not touch the plates during measurements!
11. Note down the voltage (UDMM) reading on the digital multi-meter (press DC button and set its
voltage knob at 20V).
Warning 1: There will be a voltage drop on the 220 nF capacitor because of electric discharges.
Therefore, the first value seen on the voltmeter should be taken at each measurement.
Warning 2: It is important to note that before each measurement, the parallel plate capacitor must
be discharged through contact with the free earth connecting cable, and ensure that the amplifier is
reset by pressing the leftmost button “discharge key”. Press the “discharge key” of the measuring
amplifier to discharge the capacitor (220nF) before every new measurement.
Warning 3: Be sure not to be near the capacitor during measurements, as otherwise the electric
field of the capacitor might be distorted and may cause unexpected errors in your measurements.
12. Calculate,
QAir (nAsec) = Cref x UDMM
Where Cref = 220nF
For dielectric (plastic) sheet:
13. Now, place the dielectric (plastic) sheet between the capacitor plates and make sure that the
surfaces of plates touch the sheet completely without any air gap. Secure the sheet using the Vernier
attached to the plate capacitor. Be extremely careful while placing and securing the dielectric
between the capacitor plates.
14. Repeat the steps 8 to 11 and calculate the charge Q for dielectric (plastic) sheet using the
following equation;
QPlastic (nAsec) = Cref x UDMM
Where Cref = 220nF
15. Determine the dielectric constant of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir
16. Vary the voltage from 0.5kV to 4kV in steps of 0.5kV and repeat the steps from 9 to 15. Note
down corresponding values of UDMM in case of air and dielectric material (plastic). Calculate Q in
each case using the above relations.
17. Plot the graphs between QPlastic vers UC and QAir vers UC.

Figure 6: Electric field of a plate capacitor with small distance between the plates, as compared to the
diameter of the plates. The dotted lines indicate the volume of integration.

Observations and Calculations:

Measurement of Dielectric Constant for Plastic Sheet:
Area of parallel plate capacitor (Dia = 260 mm) = A = 0.0531 m2
For plastic sheet, d (gap between plates) = 0.98 cm
Table 1: Measurement of dielectric constant for plastic sheet.
Uc (kV) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

UDMM-Plastic (V)

QPlastic (nAs)

UDMM-Air (V)

QAir (nAs)

ε = QPlastic /QAir

Note: Typical values of 𝜀 for Plastic ~ 3.

Precautions:
1. Take extreme care while operating with the high voltage supply.
2. Avoid touching of the plates while connected to high voltage supply.
3. Avoid synthetic clothing and maintain distance from the set up while performing the experiment.
4. Use short cables as much as possible. Avoid loose connections.
 National University of Technology
(NUTECH)
Initial Lab Report
Course: Applied Physics Lab (PHY1302)
Batch: Fall 2023
Department: Computer Engineering

Initial Lab Report

Experiment No. 2 Date:

Experiment Title:

Name: _______________________________

NUTECH ID: _________________________

Instructor: ____________________________

Signature (Instructor):

1. Experiment Objectives:

2. Basic Equations of Experiment Theory:

3. Observations and Calculations:
Measurement of Dielectric Constant for Plastic Sheet:
Area of parallel plate capacitor (Dia = 260 mm) = A = 0.0531 m2
For plastic sheet, d (gap between plates) = 0.98 cm
(A) At UC = 0.5kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
(B) At UC = 1kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
 ε (plastic) = QPlastic /QAir

ε (plastic) =
(C) At UC = 1.5kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
(D) At UC = 2kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
(E) At UC = 2.5kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
(F) At UC = 3kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
(G) At UC = 3.5kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
(H) At UC = 4kV
i) For Air
UDMM = V; Cref = 220nF
QAir (nAsec) = Cref x UDMM

QAir = nAsec
ii) For Plastic Sheet
UDMM = V; Cref = 220nF
QPlastic (nAsec) = Cref x UDMM

QPlastic = nAsec
Determine the dielectric constant (ε) of plastic sheet by using the following relation;
ε (plastic) = QPlastic /QAir

ε (plastic) =
Note: Finally, plot the graphs between QPlastic vers UC and QAir vers UC
Note: Typical values of 𝜀 for Plastic ~ 3.
Table 1: Measurement of dielectric constant for plastic sheet.
Uc (kV) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

UDMM-Plastic (V)

QPlastic (nAs)

UDMM-Air (V)

QAir (nAs)

ε = QPlastic /QAir
4. Results and Analysis:
 Final Lab Report Template
Title Page
The title page of your Lab report should include the following information:
a) NUTECH Logo
b) No. and Name of the Experiment
c) Submitted To: Name of the Instructor
d) Submitted By: Individual Member Name with respective registration No.s
e) Date of Experiment Performed

1. Objective:
Objective of the practical will be explained in this section. For example, this practical is used to determine
different types of strength.
2. Apparatus:
Write the name of the apparatus used in the experiment.
3. Theoretical Explanation:
Explain the theory behind the practical or experiment. It can include ideal diagrams used in theory and graphs
etc.
4. Explanation of Procedure:
Pre explanation of the practical
5. Observations and Calculations:
The Calculation and observation during the experiment which includes reading and noting down the
measurements, draw concerned tables shown in the demonstration and class lecture.
6. Results and Analysis:
In this portion, you will describe what is achieved during experiment. Analyze and discuss the practical. Use
graphical representation if any. All calculation using formulas and demonstration of graphical portion of the
practical should be explained in this section.
7. Precautions:
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8. Comments:
a) Comments about the result.
b) Whether we have achieved the desire result or not. Deduction of the practical.
c) Conclusion of the practical.