EARTH'S MAGNETIC FIELD: A PHYSICS
PROJECT REPORT
CHAPTER 1: INTRODUCTION TO EARTH'S MAGNETIC
FIELD
Our planet, Earth, is not merely a celestial body orbiting the sun; it possesses
its own intrinsic magnetic field, a phenomenon as vital to life as the
atmosphere we breathe. Often referred to as the geomagnetic field, this
invisible force envelops our planet, extending from its core far out into space.
The prevailing scientific consensus attributes the origin of Earth's magnetic
field to the geodynamo theory. This theory posits that the motion of molten
iron and nickel in the Earth's outer core, driven by convection currents and
the planet's rotation, generates electrical currents. These currents, in turn,
produce the magnetic field that surrounds us.
The significance of Earth's magnetic field cannot be overstated. It acts as a
crucial shield, deflecting the majority of charged particles emanating from the
sun, known as the solar wind. Without this magnetic protection, the solar
wind would strip away our atmosphere, rendering the planet uninhabitable.
The Earth's magnetic field is not uniform; it has regions analogous to those of
a bar magnet, with a north and south magnetic pole. However, these
magnetic poles are not precisely aligned with the geographic poles. The
angular difference between the geographic north pole and the magnetic
north pole at any given location is known as magnetic declination, a factor
that will be relevant in our experimental measurements.
CHAPTER 2: UNDERSTANDING MAGNETS AND
MAGNETIC FIELDS
At the core of our experimental investigation lies the fundamental concept of
magnetism. A magnet is a material or object that produces a magnetic field.
This field is an invisible area of influence surrounding the magnet. Magnets
possess distinct properties, most notably the existence of two types of poles:
a North pole and a South pole. These poles are always found in pairs; a
magnet cannot have an isolated pole. A key characteristic is that like poles
repel each other (North repels North, South repels South), while unlike poles
attract (North attracts South).
The influence of a magnet extends outwards in a region known as the
magnetic field. This field dictates how other magnetic materials or moving
electric charges will interact with the magnet. We often visualize magnetic
fields using magnetic field lines. These are imaginary lines that represent the
direction and strength of the magnetic field. Several important characteristics
define magnetic field lines:
• They are always drawn as closed loops, forming continuous paths.
• Outside the magnet, field lines emerge from the North pole and enter
the South pole.
• Inside the magnet, the field lines continue from the South pole back to
the North pole, completing the loop.
• The density of the field lines (how close they are to each other) indicates
the strength of the magnetic field. Where the lines are denser, the
magnetic field is stronger.
• Magnetic field lines never intersect each other.
Understanding these properties is essential as we will use a compass needle,
which itself acts as a small magnet, to map the direction of Earth's magnetic
field and observe the influence of a bar magnet.
CHAPTER 3: TOOLS AND EQUIPMENT
To effectively conduct our study of Earth's magnetic field, a specific set of
instruments and materials are required. Each component plays a crucial role
in enabling us to observe, map, and quantify magnetic phenomena. The
following is a detailed list of the equipment used, along with an explanation
of its function within the experiment:
ESSENTIAL APPARATUS:
• Bar Magnet: This is a fundamental tool. A bar magnet, typically with a
known polarity (North and South poles clearly marked), will be used to
generate a localized magnetic field. By observing its interaction with a
compass and plotting field lines, we can understand magnetic field
patterns.
• Compass Needle: A compass contains a small, freely rotating magnetic
needle that aligns itself with the local magnetic field lines. In this
experiment, it serves as our primary indicator of magnetic direction,
allowing us to trace the direction of Earth's magnetic field and the field
produced by the bar magnet.
• Plotting Compass (or regular compass): While a standard compass is
useful, a plotting compass, often mounted on a protractor base, can be
more precise for mapping field lines. If unavailable, a regular compass
used in conjunction with a protractor can achieve similar results. Its
purpose is to accurately determine the direction of the magnetic field at
various points.
• Drawing Board: A flat, rigid surface essential for providing a stable base
for placing the paper and ensuring accurate plotting of magnetic field
lines.
• White Paper: Clean sheets of paper are necessary for drawing magnetic
field lines, marking pole positions, and recording observations.
• Drawing Pins: Used to securely fasten the white paper to the drawing
board, preventing any movement during the plotting process.
• Protractor: A semicircular or circular tool marked with degrees. It is
crucial for accurately measuring angles, particularly when plotting field
lines or taking readings with the tangent galvanometer.
• Ruler: A measuring instrument used for drawing straight lines and
measuring distances. It aids in constructing diagrams and ensuring the
accurate placement of the bar magnet and compass.
TANGENT GALVANOMETER SETUP:
• Tangent Galvanometer: This is a key instrument for quantitative
measurement. It consists of a coil of wire and a compass placed at its
center. When a current flows through the coil, it produces a magnetic
field that interacts with Earth's magnetic field. By observing the
deflection of the compass needle, we can determine the strength of the
magnetic field.
• Power Source (Battery): A DC power source, such as a battery or a
regulated power supply, is required to provide a steady electric current
to the tangent galvanometer circuit.
• Rheostat: A variable resistor used to control and adjust the amount of
current flowing through the tangent galvanometer coil. This allows for
systematic variation of current to observe its effect on the magnetic
field.
• Ammeter: An instrument used to measure the electric current flowing
through the circuit. It is connected in series with the tangent
galvanometer to monitor the current precisely.
• Connecting Wires: Insulated wires are used to connect the battery,
rheostat, ammeter, and tangent galvanometer, forming a complete
electrical circuit.
CHAPTER 4: PLOTTING MAGNETIC FIELD LINES
USING A BAR MAGNET AND COMPASS
One of the fundamental ways to visualize the invisible force of magnetism is
by mapping the magnetic field lines produced by a magnet. This process
involves using a small compass needle to trace the direction of the magnetic
field at various points around a bar magnet. By carefully recording these
directions, we can then draw lines that represent the magnetic field's
orientation and relative strength. This experiment offers a direct, hands-on
understanding of how magnetic fields permeate space.
PROCEDURE FOR PLOTTING MAGNETIC FIELD LINES:
1. Prepare the Surface: Place a clean sheet of white paper on a flat
drawing board. Secure the paper using drawing pins to prevent any
movement during the experiment.
2. Position the Bar Magnet: Place the bar magnet horizontally on the
center of the paper. Carefully mark the position of the North pole and
the South pole of the bar magnet on the paper. You can do this by
bringing a compass near each end of the magnet; the end where the
compass needle's North pole points is the magnet's South pole, and
vice-versa. Alternatively, if the poles are marked, use those indications.
3. Initial Compass Placement: Bring a compass close to one of the poles of
the bar magnet, for instance, near the North pole. Observe the direction
in which the compass needle aligns itself. The North pole of the
compass needle will point along the direction of the magnetic field.
4. Marking the Direction: While keeping the compass in the same position,
mark two small dots on the paper. Place one dot at the South pole of the
compass needle and another dot at the North pole of the compass
needle. These dots indicate the direction of the magnetic field at that
specific point.
5. Moving the Compass: Carefully move the compass so that its South pole
is exactly on the second dot you just marked. Ensure the compass
needle is free to rotate and align with the magnetic field.
6. Repeat the Process: Once the compass needle settles, mark two new
dots, again representing the new positions of the South and North poles
of the needle. Continue this process, moving the compass from dot to
dot, ensuring the South pole of the needle always rests on the
previously marked dot.
7. Tracing the Field Line: Continue this step-by-step movement and
marking until the field line reaches the edge of the paper or the South
pole of the bar magnet.
8. Completing the Plot: Repeat steps 3 through 7 for several different
starting points around the bar magnet. Begin tracing lines from various
positions near the North pole, moving towards the South pole. Also,
trace lines originating from the South pole and moving towards the
North pole (representing the internal field, though primarily we focus on
external lines).
9. Drawing the Field Lines: Once you have a series of dots representing the
direction of the magnetic field, use a ruler to carefully draw smooth lines
connecting these dots. Ensure the lines are continuous.
10. Indicating Direction: Add arrowheads to each magnetic field line
pointing from the North pole to the South pole of the bar magnet,
indicating the direction of the magnetic field.
OBSERVATIONS AND IMPORTANCE OF ACCURACY:
As you plot the lines, you will observe that they emerge from the North pole
and curve around to enter the South pole. The field lines will be most densely
packed near the poles of the magnet, indicating that the magnetic field is
strongest in these regions. Conversely, the lines will be more spread out
further away from the magnet, showing a weaker field. It is crucial to be
meticulous and make small, repeated measurements. The accuracy of the
plotted field lines depends heavily on the precision with which each dot is
placed and the smoothness of the lines drawn. Any error in placing the
compass or marking the dots will propagate, leading to distorted field lines.
DIAGRAM:
[Insert Diagram Here: A clear illustration showing a bar magnet placed on
paper, with a compass positioned nearby. Several plotted magnetic field lines
should be depicted as smooth curves originating from the North pole and
terminating at the South pole, complete with arrowheads indicating direction.
The diagram should also show dots representing intermediate positions
marked by the compass.]
CHAPTER 5: ANALYZING MAGNETIC FIELD LINES
The process of plotting magnetic field lines using a compass and bar magnet
provides a visual representation of a magnetic field's structure. Interpreting
these plotted lines allows us to understand key characteristics of the field,
such as its direction and relative strength. The patterns observed offer
tangible evidence for theoretical concepts in magnetism.
INTERPRETING THE PLOTTED LINES:
The shape of the plotted magnetic field lines reveals the spatial distribution of
the magnetic force. The lines emerging from the North pole of the bar
magnet and curving to enter the South pole illustrate the directional nature of
the magnetic field. At any point along a field line, the tangent to the line
indicates the direction of the magnetic field at that specific location. The
compass needle, by aligning itself with these lines, directly demonstrates this
principle.
Furthermore, the density of the field lines—how closely packed they are—is a
direct indicator of the magnetic field's strength. Our plots should show that
the field lines are most concentrated near the poles of the bar magnet. This
increased density signifies a stronger magnetic field in these regions. As the
lines extend further from the magnet, they become more spread out,
indicating a decrease in magnetic field strength with distance.
COMPARISON WITH THEORETICAL PATTERNS:
The magnetic field lines generated by a simple bar magnet follow a
predictable, symmetrical pattern. Theoretically, the field lines form
continuous closed loops, exiting the North pole and entering the South pole
externally. Inside the magnet, they complete the loop from South to North.
The lines are expected to be most concentrated at the poles and spread out
uniformly in the equatorial regions.
Our experimental plots should closely resemble this theoretical pattern. The
characteristic curves emerging from one pole and entering the other, along
with the variation in line density, should align with the expected magnetic
field configuration. Any significant deviations from this theoretical pattern
could arise from several factors:
• Inaccurate Compass Placement: Small errors in positioning the
compass or marking dots at each step can lead to distorted line shapes.
• External Magnetic Interference: Nearby magnetic materials or even
Earth's own magnetic field (if not properly accounted for) could slightly
influence the compass needle's alignment.
• Non-Ideal Bar Magnet: Imperfections in the bar magnet itself could lead
to a slightly irregular field pattern.
• Movement During Plotting: If the paper or the magnet shifts during the
plotting process, the accuracy of the traced lines will be compromised.
Careful execution of the procedure is paramount to achieving plots that
accurately reflect the idealized magnetic field of a bar magnet.
CHAPTER 6: INTRODUCTION TO TANGENT
GALVANOMETER
To move beyond visualizing magnetic fields and into quantifying them, we
employ instruments that can measure the magnetic effects of electric
currents. The tangent galvanometer is a crucial device for this purpose. It is
an early electromechanical instrument used for measuring electric current. Its
operation is based on the principle that when a magnetic needle is placed in
the combined field of a magnetic field produced by a current-carrying coil and
the Earth's magnetic field, its deflection is related to the current.
PRINC OF THE TANGENT GALVANOMETER:
The tangent galvanometer operates on the principle that the magnetic field
produced by a current-carrying coil is proportional to the current. Specifically,
when a small magnetic needle is pivoted at the center of a circular coil, and
the plane of the coil is set vertical and perpendicular to the magnetic
meridian, the needle deflects due to the magnetic field produced by the
current. The deflection is such that the needle aligns itself with the resultant
of the Earth's magnetic field (BE) and the magnetic field produced by the coil
(BC).
According to the tangent law, if the horizontal component of Earth's magnetic
field is BE and the magnetic field produced by the coil at its center is BC, and if
the needle deflects by an angle θ from the magnetic meridian, then:
BC = BE tan(θ)
The magnetic field at the center of a circular coil of radius r, carrying a current
I, and having n turns is given by:
BC = μ0 n I / 2r
Thus, μ0 n I / 2r = BE tan(θ). This relationship allows us to calculate the current
I if BE is known, or conversely, to determine BE if the current is known.
CONSTRUCTION OF A TANGENT GALVANOMETER:
A typical tangent galvanometer consists of the following key components:
• Coil: A circular coil of copper wire, often wound on a non-magnetic
frame. The coil is usually mounted vertically and can be rotated about a
vertical axis. It has a large number of turns to produce a significant
magnetic field. The number of turns (n) and the radius (r) are important
parameters.
• Magnetic Needle: A small, light magnetic needle is pivoted horizontally
at the center of the coil. This needle is free to rotate in the horizontal
plane.
• Compass Box: The magnetic needle is housed in a compass box, which
is typically made of brass and has a glass cover to protect the needle
from air currents. The compass box is mounted directly above the center
of the coil.
• Scale: A graduated circular scale (often a semicircle) is fixed to the base,
with its center coinciding with the pivot of the magnetic needle. This
scale allows for the precise measurement of the deflection angle (θ) of
the magnetic needle.
• Leveling Screws: The base of the instrument usually has leveling screws
to ensure that the instrument is perfectly horizontal, which is crucial for
accurate readings.
• Rheostat and Battery Connections: Terminals are provided to connect
the coil to an external circuit, typically a battery, rheostat, and ammeter,
to control and supply the current.
HOW IT WORKS:
The tangent galvanometer is set up so that the plane of the coil is in the
magnetic meridian. When a current flows through the coil, it produces a
magnetic field (BC) at its center, perpendicular to the plane of the coil. The
magnetic needle at the center is influenced by both this field and the
horizontal component of the Earth's magnetic field (BE), which is aligned with
the magnetic meridian. The needle deflects to align itself with the resultant
magnetic field. The tangent law states that the tangent of the angle of
deflection (θ) is proportional to the ratio of the field produced by the coil to
the Earth's horizontal magnetic field, i.e., tan(θ) = BC / BE. By measuring the
deflection θ and knowing BE and the coil's constants, the current can be
accurately determined.
CHAPTER 7: EXPERIMENTAL SETUP FOR TANGENT
GALVANOMETER
The tangent galvanometer is a pivotal instrument in our study, enabling us to
quantitatively measure the strength of magnetic fields. To accurately use it for
investigating Earth's magnetic field, a precise experimental setup is crucial.
This involves connecting the tangent galvanometer correctly within an
electrical circuit and carefully aligning it with respect to the Earth's magnetic
field. The following details the necessary connections and alignment
procedures.
CIRCUIT CONNECTIONS:
The tangent galvanometer is integrated into a simple series circuit. The
primary components of this circuit are:
• Power Source (DC Battery): This provides the electrical energy to drive
the current through the circuit.
• Rheostat: A variable resistor used to control the magnitude of the
current flowing through the coil. By adjusting the rheostat, we can vary
the current and observe its corresponding effect on the tangent
galvanometer's reading.
• Ammeter: This instrument measures the electric current flowing
through the circuit. It must be connected in series with the tangent
galvanometer so that it registers the exact current passing through the
coil.
• Tangent Galvanometer Coil: The coil of the galvanometer, through
which the current flows, generating a magnetic field at its center.
• Connecting Wires: These are used to establish the electrical connections
between the components.
These components are connected in a series loop, ensuring that the current
from the power source flows sequentially through the rheostat, ammeter, and
the tangent galvanometer coil, before returning to the power source. The
order of the rheostat and ammeter in the series doesn't critically affect the
outcome, but it's standard practice to have the rheostat positioned to control
the current before it reaches the ammeter and galvanometer.
ALIGNMENT WITH EARTH'S MAGNETIC MERIDIAN:
The fundamental principle of the tangent galvanometer relies on the
interaction between the magnetic field produced by its coil and the Earth's
magnetic field. For the tangent law (BC = BE tan θ) to hold true, the magnetic
field produced by the coil must be perpendicular to the Earth's magnetic field
at the location of the compass needle. This is achieved by aligning the plane
of the tangent galvanometer's coil with the Earth's magnetic meridian.
The steps for achieving this alignment are:
1. Horizontal Alignment: First, ensure the base of the tangent
galvanometer is perfectly horizontal using the leveling screws. This
ensures the pivot for the magnetic needle is truly horizontal.
2. Coil Plane Alignment: The tangent galvanometer is designed so that the
plane of its vertical coil can be rotated. Initially, set the rheostat to its
maximum resistance, resulting in minimum current. With no current
flowing through the coil, the magnetic needle of the galvanometer will
align itself with the horizontal component of Earth's magnetic field,
pointing towards the magnetic north.
3. Positioning the Coil: Rotate the entire tangent galvanometer apparatus
(or just the coil assembly if it's designed to rotate independently) so that
the plane of the coil is exactly perpendicular to the direction indicated by
the magnetic needle when no current is flowing. This ensures that when
current flows, the magnetic field generated by the coil will be in the
same direction as the magnetic needle's initial alignment (i.e., along the
magnetic meridian).
4. Zero Deflection Check: Once the coil plane is perpendicular to the
magnetic meridian, and with zero current flowing, the compass needle
should show zero deflection (or minimal deflection if there are residual
magnetic fields). This confirms that the initial setup is correctly aligned
with the Earth's magnetic meridian.
Adhering to these connection and alignment procedures is paramount for
obtaining accurate and reliable measurements of magnetic field strengths
using the tangent galvanometer.
CHAPTER 8: PERFORMING THE EXPERIMENT WITH
TANGENT GALVANOMETER
With the tangent galvanometer correctly set up and aligned, we can now
proceed to the core of the quantitative measurement phase of our
experiment. This involves systematically varying the electric current flowing
through the galvanometer's coil and observing the resulting deflection of the
magnetic needle. By recording these corresponding values of current and
deflection, we gather the data necessary to analyze the magnetic field
strength and, importantly, to determine the horizontal component of Earth's
magnetic field (BE).
PROCEDURE FOR DATA COLLECTION:
1. Initial Setup Verification: Ensure the tangent galvanometer is correctly
aligned with the magnetic meridian, as described in Chapter 7. Verify
that the ammeter is functioning and properly connected in series. The
rheostat should be set to its maximum resistance, ensuring a minimal
initial current.
2. Applying Current: Close the circuit by connecting the power source.
Adjust the rheostat to introduce a small, measurable current into the
coil. The ammeter will display the precise value of this current.
3. Recording Deflection: Observe the magnetic needle of the tangent
galvanometer. The needle will deflect from its initial position (aligned
with the magnetic meridian) due to the magnetic field produced by the
current in the coil. Carefully read the angle of deflection (θ) from the
scale on the compass box. It is crucial to record the deflection for both
ends of the needle to minimize errors due to any slight eccentricity of
the pivot. The average of these two readings provides a more accurate
deflection angle.
4. Varying the Current: Systematically increase the current flowing through
the circuit by adjusting the rheostat. For each increment of current,
carefully record the new deflection angle of the magnetic needle. It is
advisable to take readings for a range of currents that produce
deflections from approximately 10 degrees to 80 degrees. Avoid very
small currents that cause minimal deflection or very large currents that
might cause the needle to swing beyond the scale or potentially damage
the equipment.
5. Taking Multiple Readings: For each specific current value, it is good
practice to take at least two or three separate readings of the deflection
angle. This helps to identify and mitigate random errors and ensures
greater reliability of the data.
6. Tabulating the Data: Organize all the recorded data in a tabular format.
The table should include columns for the serial number, the current (I) in
Amperes (as measured by the ammeter), the deflection angle (θ) in
degrees, and potentially columns for the sine and tangent of the
deflection angle, which will be used in subsequent calculations.
7. Reversing Current Direction (Optional but Recommended): To further
enhance accuracy, after taking readings for currents flowing in one
direction, reverse the connections of the battery. This reverses the
direction of the current in the coil. Repeat the process of adjusting the
rheostat and recording deflections. The deflection angle should be
similar, but noting any differences can be insightful.
PRECAUTIONS FOR ACCURATE READINGS:
• Ensure the tangent galvanometer is perfectly horizontal and correctly
aligned with the magnetic meridian.
• Avoid parallax error when reading the deflection angle from the scale.
The eye should be directly above the pointer.
• Ensure there are no external magnetic influences (like other magnets or
iron objects) near the apparatus.
• The compass needle should be light and freely rotating without friction.
• The rheostat should provide smooth and continuous variation of
resistance.
• The battery should provide a steady DC current.
SAMPLE DATA TABLE:
A well-organized data table is essential for clarity and ease of analysis:
Serial
No.
Current (I) in Amperes
(A)
Deflection Angle (θ) in
Degrees
tan(θ)
1
[Value]
[Value]
[Calculated
Value]
2
[Value]
[Value]
Serial
No.
Current (I) in Amperes
(A)
Deflection Angle (θ) in
Degrees
tan(θ)
[Calculated
Value]
This systematic approach ensures that reliable data is collected, forming the
basis for calculating the horizontal component of Earth's magnetic field.
CHAPTER 9: DATA ANALYSIS AND CALCULATION OF
EARTH'S MAGNETIC FIELD
The experimental data collected using the tangent galvanometer, comprising
various current values and their corresponding deflection angles, now serves
as the foundation for quantifying the strength of Earth's magnetic field. The
tangent law provides the theoretical link between these observed quantities
and the magnetic field we aim to measure. Through careful calculation and
graphical analysis, we can derive the horizontal component of Earth's
magnetic field (BE).
DATA PROCESSING AND CALCULATION:
The first step in analyzing the data is to process the raw readings. For each
pair of current (I) and deflection angle (θ) recorded in the data table, we need
to calculate the tangent of the deflection angle, i.e., tan(θ). This value is
crucial because, according to the tangent law:
BC = BE tan(θ)
Where BC is the magnetic field produced by the tangent galvanometer coil
and BE is the horizontal component of Earth's magnetic field.
The magnetic field at the center of a circular coil of radius r, carrying current I,
and having n turns is given by the formula:
BC = μ0 n I / 2r
Here, μ0 is the permeability of free space, a fundamental constant with a
value of 4π x 10-7 T m/A. The values of n (number of turns) and r (radius of
the coil) are specific to the tangent galvanometer used and should be known
from its specifications.
Substituting the expression for BC into the tangent law equation:
μ0 n I / 2r = BE tan(θ)
Rearranging this equation to solve for BE:
BE = (μ0 n I) / (2r tan(θ))
This formula can be used to calculate BE for each set of readings. However, a
more robust method involves graphical analysis.
GRAPHICAL ANALYSIS:
To obtain a more reliable value for BE, we can plot a graph. We rearrange the
equation BC = BE tan(θ) and substitute the expression for BC:
μ0 n I / 2r = BE tan(θ)
This can be rewritten as:
I = (BE / (μ0 n / 2r)) tan(θ)
Let K = μ0 n / 2r. This K is a constant for a given tangent galvanometer. The
equation then becomes:
I = (BE / K) tan(θ)
This equation is in the form of a straight line, y = mx, where y = I, x = tan(θ),
and m = BE / K.
Therefore, we plot a graph with the current (I) on the y-axis and the tangent
of the deflection angle (tan(θ)) on the x-axis. The points should ideally fall on a
straight line passing through the origin.
DETERMINING BE FROM THE GRAPH:
Calculate the slope (m) of the best-fit straight line obtained from the graph.
The slope is given by:
m = ΔI / Δ(tan(θ))
From the relationship m = BE / K, we can determine BE:
BE = m * K
Substituting the value of K:
BE = m * (μ0 n / 2r)
This graphical method averages out experimental errors and provides a more
accurate determination of the horizontal component of Earth's magnetic field.
SAMPLE CALCULATION USING FORMULA:
Let's assume we have a set of readings: Current I = 0.5 A, Deflection θ = 45
degrees. For the tangent galvanometer, let μ0 = 4π x 10-7 T m/A, n = 100
turns, and r = 0.05 m.
tan(45°) = 1
BE = (4π x 10-7 T m/A * 100 * 0.5 A) / (2 * 0.05 m * 1)
BE = (6.28 x 10-5 T m) / (0.1 m)
BE = 6.28 x 10-4 T or 62.8 μT.
This calculation is for a single point; the graphical method is preferred for
overall accuracy.
CHAPTER 10: DISCUSSION OF RESULTS AND
SOURCES OF ERROR
The experimental investigation into Earth's magnetic field, employing both
magnetic field line plotting and the tangent galvanometer, yielded valuable
insights. The plotted magnetic field lines visually confirmed the presence of a
magnetic field around a bar magnet, demonstrating the characteristic
patterns of field lines emerging from the North pole and entering the South
pole. The density of these lines also qualitatively indicated the variation in
field strength, being strongest near the poles.
Through the tangent galvanometer experiment, we were able to quantify the
horizontal component of Earth's magnetic field (BE). The data collected,
relating electric current to the deflection angle of the compass needle,
allowed for the calculation of BE using the tangent law. The derived value for
BE, typically on the order of 2 x 10-5 T (or 20 μT), represents the strength of
the Earth's magnetic field in the horizontal plane at our experimental location.
This value can be compared with the accepted average value for the region, if
available, to assess the accuracy of our experimental findings. A close
agreement would validate our procedure and calculations.
ANALYSIS OF SOURCES OF ERROR:
Despite careful execution, several potential sources of error could have
influenced the accuracy of our results:
• Parallax Error: When reading the deflection angle on the tangent
galvanometer's scale, a parallax error can occur if the observer's eye is
not directly in line with the needle. This can lead to inaccurate angle
measurements.
• Inaccurate Drawing and Plotting: In the magnetic field line plotting
experiment, even small inaccuracies in placing the compass and
marking the dots can lead to distorted field lines. Furthermore,
smoothing the lines with a ruler might not perfectly represent the
continuous field.
• Non-Uniformity of Bar Magnet's Field: Real bar magnets may not
produce perfectly uniform or symmetrical magnetic fields, especially if
they are not precisely manufactured or have been exposed to external
magnetic fields.
• Errors in Current Measurement: The ammeter used to measure the
current might have its own calibration errors, leading to inaccuracies in
the current values recorded.
• Improper Alignment of Tangent Galvanometer: If the tangent
galvanometer's coil plane is not perfectly aligned with the magnetic
meridian, the tangent law's assumption of perpendicularity between BC
and BE is violated, significantly impacting the calculated BE.
• External Magnetic Influences: The presence of nearby ferromagnetic
materials, electrical appliances, or even the residual magnetism in the
apparatus can interfere with the compass needle's alignment,
introducing errors in both experiments.
• Friction in Pivot: Any friction at the pivot of the compass needle in either
the plotting compass or the tangent galvanometer can hinder its free
rotation, leading to incorrect alignment.
• Variations in Earth's Magnetic Field: While assumed constant for the
duration of the experiment, Earth's magnetic field can experience minor
fluctuations.
METHODS TO MINIMIZE ERRORS:
To improve the accuracy of future experiments, the following precautions can
be taken:
• Always read the deflection angle of the tangent galvanometer by
ensuring the eye is perpendicular to the scale to avoid parallax.
• Use a fine pencil and make precise markings when plotting magnetic
field lines, and consider using a protractor to ensure accurate angles.
• Ensure the tangent galvanometer is perfectly leveled and its coil plane is
accurately aligned with the magnetic meridian.
• Perform the experiment in a location away from strong magnetic fields
or electrical equipment.
• Use a sensitive compass with a low-friction pivot.
• Take multiple readings for each current value and average them. For the
tangent galvanometer, taking readings with the current flowing in both
directions and averaging the deflection angles can help compensate for
minor misalignments.
• When plotting field lines, making smaller step movements with the
compass will result in more detailed and accurate curves.
CHAPTER 11: APPLICATIONS OF EARTH'S MAGNETIC
FIELD
The study and measurement of Earth's magnetic field are not merely
academic exercises; they have profound practical implications across various
scientific and technological domains. Understanding and harnessing the
principles of geomagnetism enables crucial applications that impact our daily
lives and our exploration of the planet and beyond.
NAVIGATION AND ORIENTATION:
Perhaps the most ubiquitous application of Earth's magnetic field is in
navigation. The magnetic compass, a simple yet indispensable tool for
centuries, relies directly on the alignment of its magnetized needle with the
Earth's local magnetic field lines. From hikers and sailors to pilots and even
astronauts, compasses provide a fundamental directional reference, allowing
for orientation even in the absence of visual landmarks or celestial cues.
Understanding magnetic declination (the difference between magnetic north
and true geographic north) is vital for precise navigation.
GEOPHYSICAL SURVEYS:
Geophysicists utilize magnetometers to conduct geophysical surveys. By
measuring variations in the Earth's magnetic field intensity and direction
across different locations, scientists can infer the subsurface geology.
Anomalies in the magnetic field can indicate the presence of mineral deposits
(like iron ore), geological structures, or even buried archaeological artifacts.
These surveys are critical for resource exploration, geological mapping, and
understanding tectonic processes.
SPACE WEATHER AND TECHNOLOGY:
Earth's magnetic field plays a critical role in protecting us from space
weather. The magnetosphere, the region dominated by Earth's magnetic
field, acts as a shield against harmful charged particles from the sun (solar
wind) and cosmic rays. Understanding the dynamics of the magnetosphere is
essential for predicting and mitigating the effects of solar storms, which can
disrupt satellite communications, damage electronics, and pose risks to
astronauts. The behavior of the aurora borealis and australis is also a direct
manifestation of the interaction between charged particles and Earth's
magnetic field.
MAGNETIC SHIELDING AND DESIGN:
Knowledge of magnetic fields is also applied in the design of sensitive
scientific instruments and technologies that require protection from external
magnetic interference. For instance, sensitive electronic equipment,
laboratories conducting magnetic measurements, and even particle
accelerators often employ magnetic shielding. This involves using materials
that can redirect or absorb magnetic fields to create a region of stable, lowfield environment.
CHAPTER 12: CONCLUSION
This project has successfully demonstrated the fundamental principles of
magnetism and the existence and characteristics of Earth's magnetic field
through practical experimentation. By employing a compass needle and bar
magnet, we were able to visually map magnetic field lines, observing their
directional properties and relative strength, which correlated well with
theoretical expectations.
Furthermore, the use of the tangent galvanometer provided a quantitative
method for measuring the strength of magnetic fields. Through careful setup,
alignment, and data collection, we were able to determine the horizontal
component of Earth's magnetic field at our location. The analysis of deflection
angles against applied currents, particularly through graphical
representation, allowed for a reliable calculation of this geomagnetic value.
The experimental results align with established physics principles, reinforcing
our understanding of how magnetic fields behave and interact. We have
gained practical experience in using scientific instruments, collecting data
meticulously, and analyzing it to draw meaningful conclusions. This project
has effectively met its objectives by illustrating the tangible presence of
Earth's magnetic field and providing a hands-on method for its scientific
study.
CHAPTER 13: BIBLIOGRAPHY AND
ACKNOWLEDGEMENTS
BIBLIOGRAPHY:
The following resources were consulted during the preparation of this project
report:
• NCERT Physics Textbook for Class XII.
• Conceptual Physics by Paul G. Hewitt.
• Fundamentals of Physics by Halliday, Resnick, and Walker.
• Websites:
◦ Physics Classroom (www.physicsclassroom.com)
◦ BYJU'S - Learn Physics (byjus.com/physics)
◦ Khan Academy - Physics (www.khanacademy.org/science/physics)
ACKNOWLEDGEMENTS:
I would like to express my sincere gratitude to my Physics teacher, [Teacher's
Name], for their invaluable guidance, support, and encouragement
throughout this project. Their expertise and patience were instrumental in
shaping my understanding of the subject matter and in the successful
execution of this experiment.
I also extend my thanks to my parents and friends for their constant
motivation and support. Finally, I am thankful to the school administration for
providing the necessary laboratory facilities and equipment required for this
project.
CHAPTER 14: APPENDIX - RAW DATA AND
CALCULATIONS
This appendix provides the detailed raw data collected during the
experiments and the intermediate calculations performed. These tables and
calculations are presented to ensure transparency and allow for verification of
the results obtained in the previous chapters.
EXPERIMENT 1: PLOTTING MAGNETIC FIELD LINES DATA
(Note: For plotting magnetic field lines, data is primarily visual. The accuracy
is assessed by the quality and consistency of the plotted lines, as discussed in
Chapter 10. No specific numerical data tables are generated here, but
observations on line density and pattern are recorded in the main body.)
EXPERIMENT 2: TANGENT GALVANOMETER READINGS
This section presents the collected data for current (I) and the corresponding
deflection angles (θ) from the tangent galvanometer experiment. The values
of n (number of turns) and r (radius of the coil) for the specific tangent
galvanometer used are:
• Number of turns, n = [Insert Value]
• Radius of the coil, r = [Insert Value] m
• Permeability of free space, μ = 4π x 10-7 T m/A
0
Table 14.1: Observed Current and Deflection Angles
Serial
No.
Current (I)
(A)
Deflection Angle (θ)
(degrees)
tan(θ)
Calculated BE
1
[Data Value]
[Data Value]
[Calculated]
[Calculated]
2
[Data Value]
[Data Value]
[Calculated]
[Calculated]
3
[Data Value]
[Data Value]
[Calculated]
[Calculated]
(T)
INTERMEDIATE CALCULATIONS:
Each value in the 'tan(θ)' column is calculated as the tangent of the
corresponding deflection angle. The values in the 'Calculated BE (T)' column
are obtained using the formula:
BE = (μ0 n I) / (2r tan(θ))
For instance, for the first row:
BE1 = ([μ0 Value] * [n Value] * [I1 Value]) / (2 * [r Value] * [tan(θ)1 Value])
[Show calculation for a few sample rows if space permits and clarity requires.]
The final value for BE is typically determined by averaging the values
calculated from each data point or, more reliably, from the slope of the I vs.
tan(θ) graph.
CHAPTER 15: APPENDIX - DIAGRAMS AND GRAPHS
This appendix is dedicated to presenting the essential visual aids that support
the findings and procedures detailed throughout this report. These diagrams
and graphs offer a clear, visual understanding of the experimental setups,
observations, and the results derived from our study of Earth's magnetic field.
DIAGRAM 1: SETUP FOR PLOTTING MAGNETIC FIELD LINES
[Placeholder for Diagram: A clear illustration showing a bar magnet placed
horizontally on a drawing board with paper. A compass is shown positioned
near the magnet, with dots marking the direction of the magnetic field.
Several smooth, curved lines with arrowheads connect these dots, originating
from the North pole and entering the South pole of the bar magnet, visually
representing the magnetic field lines.]
This diagram visually represents the process described in Chapter 4,
illustrating how a compass is used to trace the invisible magnetic field lines
around a bar magnet.
DIAGRAM 2: TANGENT GALVANOMETER SETUP
[Placeholder for Diagram: An illustration of a tangent galvanometer,
highlighting its key components: the circular coil, the pivoted magnetic
needle at the center, the compass box with a scale, and terminals for electrical
connections. The diagram should also show the galvanometer connected in a
series circuit with a battery, rheostat, and ammeter.]
As detailed in Chapter 6 and 7, this diagram clarifies the construction of the
tangent galvanometer and its integration into the experimental circuit,
essential for quantitative measurements.
GRAPH 1: CURRENT VS. TAN(Θ)
[Placeholder for Graph: A scatter plot with 'tan(θ)' on the x-axis and 'Current
(I)' on the y-axis. The plotted points should form a linear trend passing
through the origin. A best-fit straight line should be drawn through these
points. The slope of this line (m) is crucial for calculating BE.]
This graph, central to the analysis in Chapter 9, visually demonstrates the
linear relationship between the current flowing through the tangent
galvanometer coil and the tangent of the resulting deflection angle, allowing
for the calculation of Earth's horizontal magnetic field component.