Title:
ELECTRICAL FIELDS AND POTENTIALS IN THE PLATE CAPACITOR
Week:
WEEK 8
Group:
GROUP 8
Name / Matric No:
1) SARIF SALAY MANG / 1532907
2) MUHAMAD FAIZUL IRFAN BIN ZULKIFLI / 1712833
3) MUHAMMAD KHAIRUL FIRDAUS BIN ZAINUDIN / 1713693
Instructor:
ASST. PROF. DR. SITI FATIMAH BINTI NORIZAN
1
1.0 ABSTRACT
In this experiment, there are three tasks that were performed. The first task is to determine
the relationship between voltage and electric field strength with constant plate spacing. While
the second task is to find out the relationship between electric field strength and plate spacing
with constant voltage. The last part is to compute the potential with a probe as function of
position in the plate capacitor.
From the experiment, it shows that constant distance of two plates with various voltage,
the electric field is increase as increasing of voltage while with constant voltage applied and
various distance between plate the electric field is decrease as increasing of distance between
plates.
From the last part of the experiment, it show that the measured voltage is decreasing as the
distance between the one plate and the probe is increasing.
2.0 INTRODUCTION
Objective
1) To investigate the relationship between the voltage and the electric field strength with
a constant distance of two plates
2) To investigate the relationship between the distance of two plates and the electric field
with a constant voltage
3) To measure the potential as a function of position with a probe in the designated plate
capacitor.
Background
Capacitor is an electronic component that store electric charge. Capacitor is made of
two plate or two conductor that are closely separated by dielectric material. These two plates
accumulate electric charge when power supply is connected. One of the plates accumulate
positive charge while another plate accumulates negative charge. A capacitor stores energy in
the form of electrostatic between the plates. The capacitance is the amount of electric charge
stored in the capacitor at voltage of 1V. Capacitance measured in Farad, F which is 1 farad=1
coulomb per volt. The capacitance is given by
𝐶 = 𝜅𝜀0
2
𝐴
𝑑
Where κ is dielectric constant, ε0 is the permittivity of vacuum, A is the area of each
pate and d is the separation distance.
Electric field can be described as the electric force per unit charge. The charge of the
electric field can be taken as the direction of the force it would be exerted. The positive charge
of the electric field is radially outward while negative charge is vice versa. In the presence of
electric charge or the magnetic field will produce the electric field. The magnetic field must be
varying in other to produce electric field.
In the capacitor the placement of two conducting plate parallel to each other with
constant voltage will form a uniform magnetic field. Magnetic field can be described as the
infinite charges while the electric field is the approximation to the finite area of the plate of the
capacitor. If boundary disturbance due to the finite extent of the plate are disregarded the
electric field can be calculated using the following formula
𝐸=
∅1 − ∅2 ∆∅
=
𝑥2 − 𝑥1
𝑑
Where ∆∅ is the potential difference between the plates and d is the distance between the plates.
Potential different is the expression amount of potential energy per unit charge at a
specified location which represent the work involved in the transfer of a unit quantity of
electricity between two point. Potential difference is known as voltage, V.
The electrical potential also the expression of the voltage. It can be described as
potential energy arises from any collection of charge which the charge will exert a force on any
other charge. If a positive is fixed at some point and a negative charge brought close to the
positive charge it will experience the repulsive force this will resulting the potential energy.
The potential energy of the charge can be calculated by using the following formula.
3
𝑈=
𝑘𝑄𝑞
𝑟
Where k is the coulomb constant.
Equipotential lines represent the movement lines of the electric potential or the voltage. The
lines are always perpendicular to the electric field. In the capacitor the electric field lines are
perpendicular to the both plates and the equipotential lines are parallel to the plates. The dash
line at the picture below shows the equipotential lines.
Set-up
Experimental set-up for task 1 and task 2
4
Experimental set-up for Task 3
3.0 PROCEDURE
Task 1: The investigation of the relationship between the voltage and the electric field strength
with a constant distance of two plates.
1. The experiment was set-up as shown in the figure above
2. The distance between the two plate was set to 10 cm
3. The power supply was on
4. The electric field was adjusted to the zero with 0V applied voltage
5. The applied voltage was increased until 250 V
6. The measured voltage displayed on the digital multi-meter was noted down
7. The power supply was off
Task 2: To investigate the relationship between the distance of two plates and the electric field
with a constant voltage.
1. The experiment was set-up as shown in the figure above
2. The distance between the two plates was initially adjusted to 12cm
3. The power supply was on
4. The applied violated was adjusted to 200V
5. The distance between two plates was decreased with reduction of 2cm until 2cm
6. The measured voltage displayed on the digital multi-meter for each re-placement of
plate was noted down
5
7. The power supply was off
Task 3: To measure the potential as a function of position with a probe in the designated plate
capacitor.
1. The experiment was set-up as shown in the figure above
2. The distance between two plates was adjusted to 10 cm
3. The power supply was on
4. The butane cartridge was opened
5. The end of the probe was lit up with a flame of 3 to 5 mm
6. The applied voltage was adjusted to 250V
7. The probe was moved parallel to the plate by 2cm from one of the plates
8. The measured voltage displayed on the digital multi-meter for each re-placement of the
probe with flame was noted down
9. The butane cartridge was closed, and the power supply was off
4.0 RESULT
Task 1: The investigation of the relationship between various voltage and electric field strength
with a constant plate spacing of 10cm
∅1 (V)
∅2 (V)
E (kV/m)
25
2.1
0.23
50
4.3
0.46
75
7.9
0.67
100
10.7
0.89
125
13.2
1.12
150
17.4
1.33
175
18.9
1.56
200
21.9
1.78
225
24.8
2.0
250
29.2
2.21
Table 1: Various voltage and the electric field strength
6
CALCULATIONS:
∅1 = 25 V, ∅2 = 2.1 V, d = 10 cm
𝐸=
𝐸=
∆∅
𝑑
𝑉1 − 𝑉2
𝑑
25𝑉 − 2.1𝑉
𝐸=
10 ∙ 10−2 𝑚
𝐸 = 0.23 𝑘𝑉/𝑚
Graph 1
Task 2: To investigate the relationship between the distance of two plates and the electric field
with a constant voltage of 200V.
d (cm)
∅2 (V)
E (kV/m)
2.0
4.91
9.755
4.0
3.16
4.921
6.0
2.36
3.294
8.0
1.92
2.476
10.0
1.55
1.985
12.0
1.30
1.656
Table 2: The results of the calculations, with the voltage of 200V is kept constant.
7
CALCULATIONS:
∅1 = 200 V, ∅2 = 4.91 V, d = 2 cm
∆∅
𝑑
𝐸=
𝐸=
𝐸=
∅1 − ∅2
𝑑
200𝑉 − 4.91𝑉
2 ∙ 10−2 𝑚
𝐸 = 9.755 𝑘𝑉/𝑚
Electric Field Strength (kV/m)
Electric Field Strenght vs Distance
12.000
y = -0.716x + 9.0264
10.000
8.000
6.000
4.000
2.000
0.000
0
2
4
6
8
10
12
Distance (cm)
Graph 2
The values are then plotted on a log-log graph, calculated using the formula,
8
14
Log d (cm)
Log E (kV/m)
0.301
0.989
0.602
0.692
0.778
0.518
0.903
0.394
1.000
0.298
1.079
0.219
Table 3: Value of Log d and Log E
Log E vs Log d
1.200
Log E (kV/m)
1.000
y = -1.0108x + 1.3012
0.800
0.600
0.400
0.200
0.000
0
0.2
0.4
0.6
0.8
1
1.2
Log d (cm)
Graph 3
Task 3: To measure the potential as a function of position with a probe in the designated plate
capacitor.
Distance, x (cm)
ϕ0 (V)
ϕ (V)
2
250
241.94
4
250
233.88
6
250
225.82
8
250
217.76
10
250
209.7
Table 4: The measured voltage and the distance between one plate and probe. Voltage is set
at 250V with a constant distant between plates of 10cm
9
Electric Potential, ϕ vs. Distance, x
Electric Potential, ϕ (V)
245
240
235
230
225
220
215
210
y = -4.03x + 250
205
0
2
4
6
8
10
12
Distance, x (cm)
Graph 4
5.0 DISCUSSION
From the result in the table 1 it shows that the measured voltage is increase as the applied
voltage increase with constant distance between the plates. As we understood the capacitor will
store charge which conforms from this experiment the applied voltage increases and the value
charging the capacitor also increase. The electric field strength is calculated using the different
between applied voltage and measured voltage divided with the distance between two plates.
The result plotted in the graph 1 showed electric field is increasing as the voltage increase. This
result confirms the theory which electric field strength is directly proportional to the voltage.
The error that might be occur during the experiment is zero error. The zero error is reduced by
using zero balancing at the electric field meter.
From the result in the table 2 it shows that the measured voltage is decreasing as the distance
of separation between the plates is increasing with constant applied voltage. The electric field
strength was calculated using the difference between applied voltage and the measured voltage
divided distance between two plates. The result plotted in the graph 2 showed electric field is
decreasing as the distance between two plates is increasing. Then the result of electric field
strength converts to the logarithmic function as plotted in the graph 3 that showed logarithmic
of electric field is inversely proportional to the distance of two plate. This result is similar to
the theory which if the plate is closer the opposite charge attracts each other become stronger
that will produce stronger electric field strength. The error that might be occur during the
10
experiment is parallax error. This error occurs during adjustment of the plates. The plate also
difficult to place parallel to each other that contribute to parallax error. The error is reduced
with properly observe the position of the plate for each change by the eye of the observer
parallel to the reading on the optical bench.
From the result in the table 4 and graph 4 it can be seen that the electric potential is
decreasing uniformly as the distance between one plate to the probe is increase. It can be said
that the further the probe from the capacitor plate the lesser the electric potential. This showed
that the electric potential is higher near to the plate of the capacitor. This can be observed the
relationship between these two variables is inversely proportional. This can be understood that
electric potential is decreasing when I move far away from the plate due to the presence of
equipotential line. From this task the error that might be occur is the air at the tip of the probe
is not ionised properly. To reduce this error the flame is lit up to 3-5 mm long. Furthermore,
the probe is properly move parallel to the capacitor plate to get accurate result.
6.0 CONCLUSION
It can be concluded when two conducting plate placed parallel to each other will store
electric charge equivalent to the function of a capacitor. After that from the investigation of the
relationship between the electric field strength and the voltage with a constant distance of the
separation between two plate shows that it directly proportional to each other. Furthermore, it
was seen that the relationship between the electric field strength and the distance of the
separation between two plates with constant voltage applied is inversely proportional to each
other. Finally, the electric potential in the capacitor is measured using the probe showed that
the electric potential is inversely proportional to the distance between one plate to the probe.
Therefore, all objective of this experiment was achieved.
11