MARMARA UNIVERSITY
FACULTY OF ENGINEERING
PHYS 1104 PHYSICS
LABORATORY II
EXPERIMENT 6
Magnetic Field Of Solenids
Section: 2
Group: 3
Instructure: Arş. Göv. Dr. Didem Aycan
Due Date: 12.05.2025
Student ID
Number
Name & Surname
Contribution
1
Depa
rtme
nt
ChE
150623008
Remziye Kızmış
2
ChE
150623016
Gözde Balaban
3
ChE
150623030
Sude Fırçasıgüzel
Theory, Conclusion , Report
Arrangement
Tables, Calculation and Results,
Graphs
Procedure
1.TABLES
1.1. Table of Contents
1.TABLES ................................................................................................................... 2
1.1. Table of Contents ................................................................................................ 2
1.2. Table of Figures .................................................................................................. 3
2. THEORY ................................................................................................................. 4
2.1. Ampere’s Law .................................................................................................... 4
2.2. Influence of Current on the Magnetic Field ............................................................ 6
2.3. Influence of the Number of Turns ......................................................................... 6
2.4. Magnetic Field Distribution Along the Solenoid ..................................................... 6
2.5. Comparison of Experimental and Theoretical Results ............................................. 7
3. PURPOSE ................................................................................................................ 7
4.EXPERIMENTAL PROCEDURE ............................................................................... 7
4.1.Equipment List .................................................................................................... 7
4.2. Procedure ........................................................................................................... 8
4.2.1. Part 1........................................................................................................... 8
4.2.2 Part 2 ......................................................................................................... 10
5.TABLES ................................................................................................................. 10
6.CALCULATİON AND RESULTS ............................................................................ 13
Part 2 ..................................................................................................................... 13
Part3 ...................................................................................................................... 13
7.CONCLUSİON ....................................................................................................... 14
8.DATA SHEET ........................................................................................................ 15
9.REFERENCES ........................................................................................................ 15
2
1.2. Table of Figures
Figure 1 Solenoid ......................................................................................................... 4
Figure 2 Magnetic Field Lines on Solenoid ...................................................................... 4
Figure 3 ....................................................................................................................... 8
Figure 4 ....................................................................................................................... 9
Figure 5 ....................................................................................................................... 9
Figure 6 ..................................................................................................................... 12
Figure 7 ..................................................................................................................... 12
Figure 8 ..................................................................................................................... 13
Figure 9 Data sheet ..................................................................................................... 15
1.3. Table of Tables
Table 1 B values along z-axis of the solenoid................................................................. 10
Table 2 Calculated value of μ0...................................................................................... 11
Table 3 Values along current of the solenoid.................................................................. 11
3
2. THEORY
2.1. Ampere’s Law
Figure 1 Solenoid
A solenoid is a long, tightly wound coil of wire(Figure 1), often wound in a helical shape,
that generates a magnetic field when an electric current flows through it[1]. This
configuration allows for the creation of a nearly uniform magnetic field inside the solenoid,
which has applications in numerous fields, including electromagnetism, magnetic resonance
imaging (MRI), and in devices like inductors and transformers.[2]
In classical electromagnetism, the relationship between the current and the magnetic field
inside a solenoid is explained by Ampère’s Law, which describes how electric currents
produce magnetic fields.[3] The magnetic field inside an ideal, infinitely long solenoid is
uniform and directed along the axis of the solenoid, and its magnitude depends on the current
passing through the coil, the number of turns in the solenoid, and the length of the
solenoid.[4]
Figure 2 Magnetic Field Lines on Solenoid
The magnetic flux density B inside an ideal solenoid is given by the equation:
𝜇0 𝑁𝐼 = ∮ →→
𝐵 𝑑𝑙
4
𝐵=
𝜇0 𝑁𝐼
𝐿
Where:





B is the magnetic flux density, measured in teslas (T),
μ0 is the permeability of free space, which has a constant value of 4π×10−7 T.m/A,[5]
N is the total number of turns of the coil,
I is the electric current passing through the coil, measured in amperes (A),
L is the length of the solenoid, measured in meters (m).
This equation is derived under the assumption that the solenoid is sufficiently long, so that
edge effects can be neglected and the magnetic field inside the solenoid is uniform[4]. In
reality, for a finite-length solenoid, the magnetic field at the ends of the solenoid is weaker
and exhibits a non-uniform distribution[6]. However, in the middle portion of a sufficiently
long solenoid, the field is uniform and directed along the axis of the solenoid.
The magnetic field outside the solenoid is typically treated as negligible, as the majority of
the field lines are contained within the solenoid[1]. This property makes solenoids ideal for
generating controlled magnetic fields with minimal leakage.
The Hall-effect probe is used to measure the magnetic flux density in this experiment. The
Hall effect refers to the development of a transverse voltage across a conductor when it is
placed in a magnetic field, and a current is passed through it. The Hall voltage generated is
proportional to the strength of the magnetic field. A Gaussmeter is used to measure this Hall
voltage and convert it into the corresponding value of the magnetic flux density B[7].
To experimentally determine the permeability of free space μ0, we rearrange the equation for
B to:
𝜇0 =
𝐵𝐿
𝑁𝐼
Where:

B, N, I, and L are experimentally measured quantities, and μ0 is calculated.
By measuring the magnetic field strength B at various points along the solenoid, and
recording the corresponding values of current I, the number of turns N, and the solenoid
length L, the experimental value of μ0 can be determined. The theoretical value of μ0, which
is 4π×10−7 T.m/A, will then be compared with the experimental value to assess the accuracy
of the experiment.
5
2.2. Influence of Current on the Magnetic Field
One of the fundamental relationships governing solenoid behavior is the direct
proportionality between the magnetic field and the current flowing through the solenoid.
From the equation B=μ0NI/L , it is clear that as the current I increases, the magnetic flux
density B also increases, assuming all other factors (such as solenoid length and number of
turns) remain constant. This linear relationship is crucial because it allows for precise control
of the magnetic field strength by varying the current[8].
In practical applications, the ability to adjust the magnetic field by changing the current is an
important characteristic of solenoids. The experiment involves systematically varying the
current to observe how the magnetic field strength changes and to test the linear relationship
between B and I. This relationship will be confirmed experimentally by plotting B against I
and determining if the graph forms a straight line.
2.3. Influence of the Number of Turns
The number of turns N in a solenoid is another critical factor affecting the strength of the
magnetic field. From the equation B=μ0NI/L, it is evident that the magnetic field strength is
directly proportional to the number of turns in the solenoid. Increasing the number of turns
increases the total magnetic field produced for a given current[9].
This relationship suggests that solenoids with more turns will generate stronger magnetic
fields, making them more suitable for applications where a stronger magnetic field is
required. The experiment will involve solenoids with different numbers of turns (e.g., 100,
200, and 300 turns), and the corresponding magnetic field strength will be measured. By
comparing the magnetic field strengths, the effect of increasing the number of turns can be
observed experimentally.
2.4. Magnetic Field Distribution Along the Solenoid
The magnetic field inside the solenoid is uniform at the center but decreases in strength as
one moves toward the ends of the solenoid. This variation in the field strength is due to the
edge effects at the ends of the solenoid. In the central region of the solenoid, the magnetic
field is nearly uniform because the field lines are parallel to the solenoid axis and contribute
equally to the total field strength. However, near the edges, the field lines spread out and
become weaker, resulting in a non-uniform magnetic field at the ends of the solenoid[10]
In this experiment, the Hall-effect probe is moved along the axis of the solenoid to measure
the magnetic field at various points. Measurements taken near the center of the solenoid will
provide the most accurate estimate of the uniform magnetic field, while measurements taken
closer to the ends of the solenoid will show the decrease in magnetic field strength due to
edge effects.
6
To minimize these edge effects, it is important to position the Hall-effect probe near the
center of the solenoid when taking measurements of the magnetic field for calculating the
permeability of free space[11].
2.5. Comparison of Experimental and Theoretical Results
The experimental data obtained from measurements of magnetic flux density will be
compared with the theoretical predictions derived from Ampère's Law. The theoretical value
of the magnetic permeability of free space μ0 is known to be 4π×10−7 T.m/A, and by applying
the experimentally measured values of B, N, I, and L, the experimental value of μ0 can be
calculated.
The percentage error between the experimental value and the theoretical value will be
determined to evaluate the accuracy of the measurements. Any deviations from the
theoretical predictions may be attributed to experimental limitations, such as the precision of
the measuring instruments, the alignment of the probe, and the influence of external magnetic
fields.
By conducting this experiment, the relationship between magnetic field strength, current, and
solenoid parameters is explored in depth, and the accuracy of the theoretical model is verified
through direct experimental measurements.
3. PURPOSE
The aim of this experiment is to map the axial magnetic flux density B of long solenoid coils
(with 100, 200, and 300 turns) using a Hall-effect probe and Gaussmeter, and from these
measurements to determine the vacuum permeability μ0. In practice, we will measure B along
the central z-axis of each solenoid for a fixed current, as well as B at the solenoid’s center
while varying the current. These data allow comparison with the theoretical solenoid field
law and extraction of μ0. In other words, the experiment “investigates the magnetic field
distribution created by [a solenoid] using Hall probe and Gauss meter in order to determine
the constant μ0. The experimental value of μ0 will be obtained by fitting the measurements to
the relation predicted by Ampère’s law, and then compared to its known value (~1.26×106
·m/A)
4.EXPERIMENTAL PROCEDURE
4.1.Equipment List
1. DC Voltage Source (0 – 30 V range) x1
2. Connection cables
3. Digital Multimeter x1
4. G-clamp x1
7
5. Gaussmeter with DC Hall Probe x1
6. Right angle clamp x1
7. 100 turns solenoids (L=0,043m) x1
8. Support rod x1
9. 200 turns solenoids (L=0,090m) x1
10.Ruler x1
11.200 turns solenoids (L=0,143m) x1
4.2. Procedure
4.2.1. Part 1
Figure 3
1. The experimental circuit was set up for the 100-turn solenoid as shown in Figure 3.
2. The multimeter was adjusted to function as an ammeter with a 10A scale.
3. The switch on the left side of the teslameter (gaussmeter) was set to the
‘SIFIRLAMA’ position (see Figure 4).
8
Figure 4
4. The black knob on the right side was turned until the digital display read “0.00”.
5. Then, the switch was moved to the ‘ÖLÇME’ position, and the magnetic field
intensity along the solenoid’s axis was measured (see Figure 5).
Figure 5
6. Before starting the measurements, it was ensured that the probe was aligned at the
center of the solenoid.
7. The power supply was set to 12 V.
8. The slider of the rheostat was adjusted until the current measured by the multimeter
reached 0.5 A.
9. The magnetic field was measured by moving the solenoid from its input (z = 0) to its
output at regular intervals. The measured values were recorded in Table 1.
10. A graph of z (cm) versus B(z) was plotted using the data from Table 1.
11. The magnetic field value at the center of the solenoid was measured and recorded in
Table 2.
12. The experimental value of μ₀ was calculated using Equation 2.
13. The percentage error between the theoretical and experimental values of μ₀ was
calculated and recorded in Table 2.
14. The same procedure was repeated for solenoids with 200 and 300 turns, respectively.
9
4.2.2 Part 2
1. The experimental setup for the 200-turn solenoid was built in the same manner as in
Part 1.
2. The Hall effect probe was placed at the midpoint of the solenoid, and the current was
set to 0 A.
3. The current was gradually increased up to 1.0 A in 10 steps. The corresponding
magnetic field values were recorded in Table 3.
4. A graph of current versus magnetic field intensity was plotted based on the values in
Table 3.
5. The equation of the plot was obtained by curve fitting to determine the slope of the
line.
6. The magnetic permeability was calculated using the slope of the line and compared
with the theoretical value.
5.TABLES
Table 1 B values along z-axis of the solenoid
Z(cm)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
N1=100
1.1
0.8
0.5
0.1
0
0
0.2
0.7
0.7
1
1.1
N2=200
0.1
0.4
0.6
1
1.2
1.4
1.6
1.6
1.6
1.4
1.2
1
0.6
0.2
0.2
0.1
N3=300
0
0.2
0.5
1
1.3
1.5
1.5
1.5
1.5
1.5
1.7
1.7
1.5
1.5
1.5
1.5
1.2
10
17
18
19
20
1
0.5
0.2
0
Table 2 Calculated value of μ0
H
L
Bmiddle
125MH
8.5
0.2
560MH
14
1.6
600MH
19
1.7
𝜇0
3.4 10−7
%73.02
2.24 10−6
%77.78
2.15 10−6
%70.90
%error
Table 3 Values along current of the solenoid
I(A)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
B(mT)
0
0.3
0.5
1
1.2
1.5
1.8
2.0
2.5
3.0
𝜇0
%error
1.14 10−6
%9.52
11
N1=100 vs Z
1,2
N1=100
1
0,8
0,6
N1=100
0,4
Линейная (N1=100)
0,2
0
0
5
10
15
Z (cm)
20
25
Figure 6
o
y = 0.0036·Z + 0.5391
o
Slope: 0.0036
N2=200
N2=200 vs Z
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
N2=200
Линейная (N2=200)
0
5
10
15
Z (cm)
20
Figure 7
o
y = -0.02·Z + 1.0375
o
Slope: -0.02
12
25
N3=300
N3=300 vs Z
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
N3=300
Линейная (N3=300)
0
5
10
15
Z (cm)
20
25
Figure 8
o
y = -0.00052·Z + 1.0909
o
Slope= -0.00052
6.CALCULATİON AND RESULTS
Part 2
μ₀ = (B × L) / (N × I)
For N1 = 100 turns:
B = 0.0002 T, L = 0.085 m, N = 100
μ₀ = (0.0002 × 0.085) / (100 × 0.5) = 3.40 × 10⁻⁷ T·m/A
% error = |(3.40×10⁻⁷ - 1.26×10⁻⁶) / 1.26×10⁻⁶| × 100 = 73.02%
For N2 = 200 turns:
B = 0.0016 T, L = 0.14 m, N = 200
μ₀ = (0.0016 × 0.14) / (200 × 0.5) = 2.24 × 10⁻⁶ T·m/A
% error = |(2.24×10⁻⁶ - 1.26×10⁻⁶) / 1.26×10⁻⁶| × 100 = 77.78%
For N3 = 300 turns:
B = 0.0017 T, L = 0.19 m, N = 300
μ₀ = (0.0017 × 0.19) / (300 × 0.5) = 2.15 × 10⁻⁶ T·m/A
% error = |(2.15×10⁻⁶ - 1.26×10⁻⁶) / 1.26×10⁻⁶| × 100 = 70.90%
Part3
B = 0.0036·I + 0.5391 (slope in T/A)
13
μ₀ = (slope × L) / N
slope = 0.0036 T/A, L = 0.19 m, N = 600
μ₀ = (0.0036 × 0.19) / 600 = 1.14 × 10⁻⁶ T·m/A
% error = |(1.14×10⁻⁶ - 1.26×10⁻⁶) / 1.26×10⁻⁶| × 100 = 9.52%
7.CONCLUSİON
In this experiment, the magnetic field distribution along the axis of solenoids with different
numbers of turns was investigated, and the magnetic permeability of free space was
determined experimentally. Measurements were performed using a Hall effect probe for
solenoids with 100, 200, and 300 turns at a constant current of 0.5 A. Additionally, the
relationship between the magnetic field and the current was analyzed for the 300-turn
solenoid.
The experimentally calculated values of were found to be , , and for N = 100, 200, and 300
turns, respectively. These values deviate significantly from the theoretical value of , with
percentage errors of 73.02%, 77.78%, and 70.90%. The large errors can be attributed to edge
effects, misalignment of the Hall probe, and possible external magnetic interference.
Other possible sources of error include inaccurate calibration of the Gaussmeter, fluctuations
in the power supply voltage affecting the current stability, imperfect centering of the probe
inside the solenoid, mechanical instability or tilting of the probe setup, and manual reading
errors. Additionally, assuming a perfectly uniform magnetic field in the solenoid may not
hold true near the ends, further contributing to deviations.
In Part 2, a linear relationship between magnetic field intensity and current was observed.
Linear regression analysis of the data yielded the relation:
B=0.00319⋅I−5.45×10−5
with a high correlation coefficient , indicating a strong linear fit. Using the slope and the
solenoid parameters (L = 0.19 m, N = 600), the permeability was recalculated as:
μ0=0.00319⋅0.19 /600=1.01×10−6T.m/A
This result has a much smaller error of 19.84%, which demonstrates that analyzing the relationship provides a more accurate determination of .
Overall, the experiment successfully demonstrated the fundamental behavior of magnetic
fields inside solenoids and provided insight into the practical determination of physical
constants, while highlighting the importance of minimizing systematic errors in laboratory
measurements.
14
8.DATA SHEET
Figure 9 Data sheet
9.REFERENCES
Figure 1. https://tr.wikipedia.org/wiki/Dosya:Solenoid-1.png
Figure 2. https://www.miniphysics.com/wp-content/uploads/2012/07/solenoid-magneticfield.jpg
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University Press.
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3. Griffiths, D. J. (2013). Introduction to Electrodynamics (4th ed.). Pearson.
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5. Feynman, R. P., Leighton, R. B., & Sands, M. (2011). The Feynman Lectures on Physics:
Volume II (2nd ed.). Addison-Wesley.
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Pergamon Press.
7. Halls, C. S., & Gaskins, S. H. (2012). Principles of Experimental Physics (6th ed.). Wiley.
8. Tipler, P. A., & Mosca, G. (2007). Physics for Scientists and Engineers (6th ed.). W. H.
Freeman.
9. Ramo, S., Whinnery, J. R., & Van Duzer, T. (1994). Fields and Waves in Communication
Electronics (3rd ed.). Wiley.
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11. Sears, F. W., & Zemansky, M. W. (1964). University Physics (5th ed.). Addison-Wesley.
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