TEP
Magnetic field of single coils with Cobra4
Related topics
Biot-Savart’s law, Hall effect, magnetic field, induction, magnetic flux density.
Principle
The magnetic field along the axis of coils of different dimensions is measured with a Cobra4 Sensor-Unit
Tesla and a Hall probe. The relationship between the maximum field strength and the dimensions is investigated and a comparison is made between the measured and the theoretical effects of position.
Equipment
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Cobra4 Wireless Manager
Cobra4 Wireless-Link
Cobra4 Sensor-Unit Tesla
Cobra4 Sensor-Unit Motion
Cobra4 Sensor-Unit Electricity
Holder for Cobra4 with support rod
Induction coil, 300 turns, d = 40 mm
Induction coil, 300 turns, d = 32 mm
Induction coil, 300 turns, d = 25 mm
Induction coil, 200 turns, d = 40 mm
Induction coil, 100 turns, d = 40 mm
Induction coil, 150 turns, d = 25 mm
Induction coil, 75 turns, d = 25 mm
Hall probe, axial
Power supply, universal
Fig. 1:
12600-00
12601-00
12652-00
12649-00
12644-00
12680-00
11006-01
11006-02
11006-03
11006-04
11006-05
11006-06
11006-07
13610-01
13500-93
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Meter scale, demo. l =1000 mm
03001-00
Barrel base PHYWE
02006-55
Support rod PHYWE, square, l = 250 mm 02025-55
Right angle clamp PHYWE
02040-55
Lab jack, 200×230 mm
02074-01
Connecting cord, l = 500 mm, red
07361-01
Connecting cord, l = 500 mm, blue
07361-04
Bench clamp PHYWE
02010-00
Stand tube
02060-00
Screen, metal, 300×300 mm
08062-00
Software measure for Cobra4
14550-61
Additionally required
PC with USB interface, Windows XP or
1
higher
Experimental set-up.
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1
TEP
Magnetic field of single coils with Cobra4
Task
Measure the magnetic flux density along the axis of long coils and compare it with theoretical values.
Set-up and procedure
Connect the Sensor-Unit Electricity to one Wireless-Link. Select an appropriate current e.g. the maximum current indicated on the coils using the power supply as a constant current supply. The power supply is in the constant current mode when the red LED above the current control is on. Set the voltage
control sufficiently high as to achieve this. Else the power supply is in the constant voltage mode and the
current will decrease with the warming of the coils and this may disturb your measurement. 1200 mA
may be chosen for all the solenoid coils. Once you have adjusted the current, you may leave the current
control untouched so as to measure all the coils with the same current. But do turn down the voltage before you break the circuit unplugging the coils to avoid spikes (!).
Now connect the Sensor-Unit Tesla to this Wireless-Link and to the Hall probe. Connect the Sensor-Unit
Motion to the other Wireless-Link.
Set up the experiment according to Fig. 1, start the “measure” program on your computer and load the
“Biot-Savart’s law” experiment. (Experiment > Open experiment). All pre-settings that are necessary for
measured value recording are now carried out.
Measure the magnetic field strength along the z-axis of the solenoid coils sliding the Hall probe mounted
to a barrel base along the meter and recording the position with the motion sensor. If you keep the barrel
base sliding on just one edge of the meter, you can achieve a fairly straight movement through the centre of the coils.
Click on
in the icon strip to start measurement and slide the Hall probe
along the meter for about 40 cm. Click on the
icon in the icon strip to
end measurement and send the data to measure (Fig. 2).
Plot the results for
- same diameter and denstiy of turns but different length of coil (Fig. 3)
Fig. 2: Saving measurements.
- same density of turns and length but different diameter (Fig. 4)
- same length and diameter but different density of turns (Fig. 5)
The plots may look as the following diagrams:
Fig.. 3:
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Dependance on coil length of the magnetic field with same density for 1200 mA
current and 41 mm coil diameter.
PHYWE Systeme GmbH & Co. KG © All rights reserved
P2430260
Magnetic field of single coils with Cobra4
Fig.. 4:
Independence on coil diameter of field strength with 1200 mA current and
165 mm coil length.
Fig.. 5:
Linear dependence on number of turns of field strength for 1200 mA current
and 26 mm coil diameter.
TEP
Theory and evaluation
Magnetic field along the axis of a (long) coil
The calculation of the magnetic flux density on the axis of a uniformly wound coil of length l and with n
turns yields the result
For the middle of the coil, z = 0 follows
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PHYWE Systeme GmbH & Co. KG © All rights reserved
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TEP
Magnetic field of single coils with Cobra4
For a long coil (l >> R), a solenoid, the upper equation finally reduce to
Therefore the magnetic field strength is for solenoids independent from the coil diameter.
The independence on the coil diameter can directly be seen in Fig. 4 whereas the dependence on number of turns is shown in Fig. 5.
Plot B (z) of equation (10) with data of the used solenoid coil with 41 mm and compare with the measured results.
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