Magnetic Fields
BACKGROUND AND THEORY
In this activity, you will examine the magnetic field of the earth and those fields produced by
electric currents in a long straight wire and in some common coil configurations.
The earth’s magnetic field is the result of the circulation of a slightly charged molten iron core.
The resulting field configuration is that of a magnetic dipole modified by iron ore bodies. At our
latitude on the earth’s surface the magnetic field lines enter the surface at quite a steep angle
relative to the horizontal.
When an electric current flows through a wire, a magnetic field is produced around the wire. The
magnitude and direction of the field depends on the shape of the wire and the direction and
magnitude of the current through the wire. If the wire is wrapped into a loop, the field near the
center of the loop is perpendicular to the plane of the loop. When the wire is looped a number of
times to form a coil, the magnetic field at the center increases.
For of a long straight conductor carrying a current I the magnetic flux density B, at a
perpendicular distance r, from the centre of it, is given by:
B=
µ0 I
2πr
where µ0 is the permeability of the vacuum, defined as 4π×10-7 Wb A-1 m-1. The permeability of
€
the air is indistinguishably different.
For a single coil of mean loop radius R, with a total number N of loops, and when a current I
passes through it, the magnitude of the magnetic field B at the centre of it is given by:
B=
µ0 NI
2R
Helmholtz coils are often used to produce a field that is uniform over a large volume. They
consist of two identical coils on
€ a common axis that are separated by a distance equal to the coil
radius. For the Helmholtz coils (or double coils) we have:
B=
OBJECTIVES
4 µ0 NI
125R
€
Use a Magnetic Field Sensor to measure the magnetic field of the Earth in your lab room.
Measure the field at the center of a single coil as a function of the current.
• Measure the field along the longitudinal axis between the two coils of a Helmholtz system.
• Examine the magnetic field around a long straight conductor and calculate the permeability
of the air, µ0.
•
•
Physics with Vernier
25 - 1
MATERIALS
Computer
Vernier computer interface
Logger Pro
Vernier Magnetic Field Sensor
Adjustable power supply
Single Coil
Helmholtz Coils
Long Straight Conductor
Magnetic compass
INITIAL SETUP
The Magnetic Field Sensor uses a Hall-effect transducer. It produces a voltage that is linear
with the magnetic field. The sensor measures only the component of the magnetic field that is
perpendicular to the white dot on the end of the sensor tip. Therefore, the reading is positive
only when the white dot on the sensor points toward a magnetic south pole.
The switch on the sensor shaft is used to select the range. The 6.4 mT range is used to
measure relatively strong magnetic fields around permanent magnets and electromagnets
(Part II and Part III). The 0.3 mT range is used mainly to measure the magnetic field of the
Earth (Part I) and other very weak fields like that of a linear current (Part IV). Note that the
north pole of a compass points toward north, since the magnetic pole of the Earth in the
northern hemisphere is a south magnetic pole!
1. Connect the Vernier Magnetic Field Sensor to Channel 1 of the interface. Set the switch
on the sensor to 0.3 mT (high amplification).
2. Open the file “25 Magnetic Field in a Coil” in the Physics with Vernier folder.
PART I: MEASURE THE MAGNETIC FIELD OF THE EARTH IN YOUR
LAB ROOM
PRELIMINARY QUESTIONS AND ADDITIONAL SETUP
1. Hold the plastic rod containing the Magnetic Field Sensor vertically with the tip of the probe
pointing horizontally. Click
to begin data collection. Slowly, rotate the rod around a
vertical axis. Look at the graph. What do you observe? What is causing the variation of field
reading?
2. Determine the orientation of the sensor when the magnetic field is at a maximum, and
compare the direction that the dot on the sensor is pointing with the direction that the
magnetic compass needle points. What did you discover? How much does the reading change
in one rotation?
Physics with Vernier
25 - 2
PROCEDURE
1. Record in the data table below, the magnitude of the magnetic field and its direction, while
pointing the tip of the Magnetic Field Sensor in the North-South, East-West and Up-Down
directions.
DATA TABLE
Part I
Geographical
direction
Magnetic field
(mT)
Component
Direction
(+/-)
Magnetic field
magnitude (mT)
Magnetic field
overall
direction
North - > South
East - > West
Up - > Down
ANALYSIS
1. Calculate the overall magnetic field magnitude and its direction and record them in the
last two columns of the data table above. For direction give the angle to the east (or west)
of geographic north, and the angle below the horizontal.
2. Compare the direction of the projection of this magnetic field vector on the horizontal
plane (the angle to the east (or west) of geographic north) with the direction of the
compass.
PART II: DETERMINE THE RELATIONSHIP BETWEEN THE MAGNETIC
FIELD AT THE CENTER OF A SINGLE COIL AND THE CURRENT
THROUGH THE COIL
PROCEDURE
1. Connect the single coil to the power supply but leave the current off except when making a
measurement.
2. Set the power supply so that the current will be maximum 2 A when the switch is
closed. Set the switch on the sensor to 6.4 mT
3. Place the shaft of the Magnetic Field Sensor in a vertical position, with the tip pointing
horizontally, so that its flat end is at the center of the coil. With the switch closed, rotate the
sensor about a vertical axis and observe the magnetic field values in the meter. Find the
position that indicates a maximum positive magnetic field. The flat end of the sensor should
be in the plane of the coil. Keep the sensor in the same position for the remainder of the
experiment.
4. We need to first “zero” the sensor when no current is flowing; by doing that, we will remove
the effect of the Earth’s magnetic field and any local magnetism. With the switch open, click
.
5. Click
to begin data collection. Wait a few seconds and then close the switch until
data collection ends.
6. View the field vs. time graph and determine when the current was flowing in the wire. Select
this region on the graph, by dragging over it. Determine the average field while the current
was on by clicking on the Statistics button, . Record the average field and the current
through the coil in the data table.
Physics with Vernier
25 - 3
6. Briefly close the switch and decrease the current by 0.25 A. and repeat Steps 4 and 5.
7. Repeat steps 4, 5 and 6 down to a minimum of 0.25 A.
DATA TABLE
Part II
Current in coil
(A)
Magnetic field
(mT)
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
ANALYSIS
Part II
1. Plot a graph of magnetic field vs. current through the coil. Use Logger Pro or another
graphing tool. Page 2 of the experiment file is set up for this graph.
2. What is the relationship between the resulting magnetic field at the center of a coil and
the current in the coil?
PART III: MEASURE THE MAGNETIC FIELD ALONG THE
LONGITUDINAL AXIS BETWEEN THE TWO COILS OF A HELMHOLTZ
SYSTEM
PROCEDURE
1. Connect both coils to build a Helmholtz system to the power supply but leave the current off
except when making a measurement.
2. Set the power supply so that the current will be maximum 2 A when the switch is closed.
3. Place the shaft of the Magnetic Field Sensor in a horizontal position, with the tip pointing
horizontally, so that its flat end is at the center of one of the coils. Keep the sensor in the
same position for the remainder of the experiment.
4. “Zero” the sensor with no current flowing through the system; by doing that, you will remove
the effect of the Earth’s magnetic field and any local magnetism. With the switch open, click
.
5. Click
to begin data collection. Wait a few seconds and then close the switch until
data collection ends.
6. View the field vs. time graph and determine when the current was flowing in the wire. Select
this region on the graph, by dragging over it. Determine the average field while the current
Physics with Vernier
25 - 4
was on by clicking on the Statistics button,
through the coil in the data table.
. Record the average field and the current
6. Briefly close the switch and move the sensor’s flat end by 1 cm toward the other coil and
repeat Steps 4 and 5.
7. Repeat steps 4, 5 and 6 until your reach the plane of the other coil.
DATA TABLE
Part III
Current through the
coils
(A)
Distance between the
sensor and one of the
coils
(m)
Magnetic field
(mT)
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
ANALYSIS
Part III
3. Plot a graph of magnetic field vs. distance between the two coils. Use Logger Pro or
another graphing tool. Page 2 of the experiment file is set up for this graph.
4. What is the relationship between the resulting magnetic between the two coils and the
position of a point between the coils?
PART IV: MEASURE THE MAGNETIC FIELD AROUND A LONG
STRAIGHT CONDUCTOR AND CALCULATE THE VALUE OF µ 0
PROCEDURE
1. Connect long straight conductor to the power supply but leave the current off except when
making a measurement.
2. Set the power supply so that the current will be maximum 3 A when the switch is
closed. Set the switch on the sensor back to 0.3 mT.
3. Place the shaft of the Magnetic Field Sensor in a position perpendicular to the linear
conductor, with the tip pointing perpendicularly to the shaft, so that the lines of field will be
Physics with Vernier
25 - 5
perpendicular to its flat end. Keep the sensor in the same position for the remainder of the
experiment.
4. “Zero” the sensor with no current flowing through the conductor; by doing that, you will
remove the effect of the Earth’s magnetic field and any local magnetism. With the switch
open, click
.
5. Click
to begin data collection. Wait a few seconds and then close the switch until
data collection ends.
6. View the field vs. time graph and determine when the current was flowing in the wire. Select
this region on the graph, by dragging over it. Determine the average field while the current
was on by clicking on the Statistics button, . Record the average field and the current
through the coil in the data table.
6. Move the sensor’s flat end by 1 cm away from the conductor and repeat Steps 4 and 5.
7. Repeat steps 4, 5 and 6 until you reach a position 5 cm away from the center of the
conductor.
8. Finally, try moving the sensor in a direction parallel to the conductor, keeping the same
distance from the centre of the conductor and collect magnetic field data to convince yourself
that the magnetic field is not changing in a direction parallel to the conductor.
DATA TABLE
Part IV
Current through the
straight conductor
(A)
Distance from the
sensor and
center of the conductor
(cm)
Magnetic field
(mT)
1.0
1.5
2.0
2.5
3
3.0
3.5
4.0
4.5
5.0
ANALYSIS
Part IV
5. Plot a graph of magnetic field vs. the reciprocal of the distance from the center of the
conductor. Use Logger Pro or another graphing tool. Page 2 of the experiment file is set
up for this graph.
6. Calculate the permeability of the air from the slope of this graph. How does it compare
with the permeability of the vacuum?
Physics with Vernier
25 - 6