Electromagnetic induction with Cobra4
TEP
Related Topics
Magnetic field, induction, field strength.
Principle
A magnetic field of variable frequency and varying strength is produced in a long coil. The voltages induced across thin coils which are pushed into the long coil are determined as a function of frequency
and field strength of the magnetic field and the number of turns and the cross-section of the induction
coil.
Material
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2
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Cobra4 Wireless Manager
Cobra4 Wireless-Link
Cobra4 Sensor-Unit Electricity,  6 A,  30 V
Digital Function Generator, 0.1 Hz...1 MHz
Field coil, 750 mm, 485 turns/m
Induction coil, 300 turns, dia. 40 mm
Induction coil, 300 turns, dia. 32 mm
Induction coil, 300 turns, dia. 25 mm
Induction coil, 200 turns, dia. 40 mm
Induction coil, 100 turns, dia. 40 mm
Induction coil, 150 turns, dia. 25 mm
Induction coil, 75 turns, dia. 25 mm
Connecting cord, 32 A, 750 mm, red
Connecting cord, 32 A, 750 mm, blue
Connecting cord, 32 A, 2000 mm, blue
12600-00
12601-00
12644-00
13654-99
11001-00
11006-01
11006-02
11006-03
11006-04
11006-05
11006-06
11006-07
07362-01
07362-04
07365-04
Additional material
1 PC with 2 USB ports, Windows XP or higher
Fig. 1:
Experimental set-up.
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Electromagnetic induction with Cobra4
TEP
Set-up
Set up the experiment in accordance with Fig. 1 the field generating coil is connected to the function
generator. The current in the field generating coil is measured with the Cobra4 Sensor-Unit Electricity.
The induction coils are connected to the voltage sockets of the Cobra4 Sensor-Unit Electricity and to
be put into the middle of the field generating coil.
Procedure
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Start the PC and Windows.
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Plug the Cobra4 Wireless Manager in the USB port of the PC.
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Connect the Digital Function Generator via its USB-port on the front panel to the USB port of the PC.
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Start the measure software package on the PC.
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Attache the Cobra4 Sensor-Unit Electricity to the Cobra4 Wireless-Link and switch it on. The sensor
is now automatically recognized and is allotted an ID-number (01) that is shown in the Cobra4 Wireless-Link display. Communication between the Cobra4 Wireless Manager and the Cobra4 WirelessLink is shown by the Data LED.
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Switch on the Digital Function Generator, which will be automatically recognized. Communication
between Measure and the Digital Function Generator is shown by the USB-Port LED.
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Load the experiment (Experiment > Open experiment > Electromagnetic induction). All necessary
settings for the recording of measured values will now be started.
Open the Setup of the Digital Function Generator and make certain that the Signal is Sinus, frequency is 1kHz and the Amplitude 5V for the beginning.
Insert the first induction coil into the center of the field generating coil.
Watch the digital display of current and voltage. They should oscillate around zero. If they don’t,
tune the “offset” at the function generator. An offset can be set but is not necessary.
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Start the measurement recording in measure with  until you see app. 10 oscillations then end the
measurement with . Choose “send all data to measure”.
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Repeat the measurement in total of four Amplitudes from 5 V to 20 V in 5 V steps.
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Repeat this measurement for all 7 induction coils.
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For induction coil 11007-01, set the amplitude to 10 V and the frequency to 1 kHz for maintaining the
same Current both values have to be changed. Start and stop measurement like before for
10 V and 1 kHz, 13 V and 1.3 kHz, 15 V and 1.5 kHz, 17 V and 1.7 kHz, 20 V and 2.0 kHz.
Fig. 2:
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Example: measurement of current (red) in the field generating coil and voltage (blue) in the induction coil.
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Electromagnetic induction with Cobra4
TEP
Results and Evaluation
For the first part the obtained data for each induction coil looks like Fig. 2. As you know is the field
strength in the field generating coil proportional to the current:
n
B(t) = µ0 ∙ I(t)
l
With µ0 the permeability constant, 𝑛 the number of turns and 𝑙 the length of the coil.
If you look at one of the measurements, for example coil 01 with amplitude of 5 V, it can clearly be seen
that a change of current induces a change in voltage.
There is a linear relationship between the current in the field generating coil and the voltage in the induction coil. The proportionality factor depends on certain properties of the induction coil. To investigate the
dependencies is the task of this experiment.
Fig. 3: „Mark“-tool and fitting results.
Fig. 4: Fit of sinus oscillation and new parameters.
First, the slope 𝑎 of the voltage response for each of the coils is to be determined:
Because of the linear relationship between current and voltage it is sufficient to determine some effective values of Current and Voltage out of the four measurements for each coil.
(Note: When working with alternating current the effective values are of interest, whereas here the
peak values can be determined, because it results in the same slope).
Open the measurements for one coil and mark several oscillations with “Mark” tool (Fig. 3) and fit
a sinus with “Function fitting” tool
to Current and Voltage (Fig. 4). Note down the amplitude 𝑎 for
both values.
For each coil enter the data
manually “Measurement” > “Enter data manually” to plot the
voltage response (Fig. 5). Evaluate the slope 𝑎 for each of the
induction coils by using the
Function
fitting” tool
and
note it down.
Fig. 5: Voltage response for coil 11006-01 with linear fit 𝒎 = 𝟏. 𝟓 V/A .
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TEP
-
Electromagnetic induction with Cobra4
The obtained diagrams for each of the induction coils can be put into one single diagram with
“Measurement” > “Adopt channel”. Here the next to last opened diagram can be loaded in the last
opened diagram and scaled to the same value with “Scale curves” > “fit collectively”
(). At “Display options”
the title can be changed for each of the measurements, note down the number of
the induction coil, number of turns 𝑛, diameter 𝑑 and slope 𝑎.
Fig. 6: Common fit of voltage response for all coils.
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Plot the response voltage per mA for induction coils with the same diameter 𝑑 but different number
of turns 𝑛 vs. the number of turns 𝑛.
Then plot the response voltage per mA for induction coils with the same number of turns 𝑛 but different diameters 𝑑 vs. the cross-section area 𝐴 corresponding to the diameter 𝑑, with
𝑑 2
𝐴=( ) ∙𝜋
2
Fig. 7 and Fig. 8 show possible results.
Fig. 7:
4
Voltage response vs. number of turns for con
stant cross-section area d=26 mm and
A=40.8 mm².
Fig. 8:
Voltage response vs. Cross-section area for
constant number of turns n=300.
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TEP
Electromagnetic induction with Cobra4
As result of the first part of the experiment, it can be observed that the induced voltage 𝑈𝑖𝑛𝑑 is proportional to: The number of turns n of the induction coil
The cross-sectional area A of the induction coil
𝑈𝑖𝑛𝑑 ∝ 𝑛 ∙ 𝐴
For the second part the obtained data looks like the data in Fig. 2 again. The amplitude of the voltage
needs to be changed for measuring the same current in the field generating coil. As well the frequency is
changed.
Determine the voltage of all measurements for coil 11007-01, by fitting a sinus oscillation like before.
Reassure that the current of all measurements is the same.
Use “Measurement” > “Enter data manually” to plot the frequency dependence of the voltage, as is
seen in Fig. 9.
Fig. 9 shows:
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Fig. 9: Voltage response vs frequency.
The higher the frequency of the magnetic field, the higher the induced voltage. In Fig. 5 it can be seen
that the induced voltage is also proportional to the amplitude of the magnetic field. That means, the induced voltage is proportional to the time rate of change of the magnetic field:
𝑈𝑖𝑛𝑑 ∝
𝑑𝐵
𝑑𝑡
with
𝑑𝐵
𝑑
𝑛
𝑑
𝑛
𝑛
= (µ0 ∙ 𝐼(𝑡)) =
(µ0 ∙ 𝐼0 sin(ωt)) = 𝐼0 𝜔µ0 cos(ωt)
𝑑𝑡 𝑑𝑡
𝑙
𝑑𝑡
𝑙
𝑙
With these results, the induced voltage can be calculated:
𝑈𝑖𝑛𝑑 = 𝑛 ∙ 𝐴 ∙
𝑑𝐵
𝑑𝑡
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TEP
Electromagnetic induction with Cobra4
Room for notes:
6
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