Exp9 Electromagnetic Fields PDF

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Department of Engineering Technology University of Ruhuna ENT1221: Common Practical III (Electricity and Magnetism) Experiment-9: Electromagnetic Fields Objectives:  

To measure the electromagnetic field strength of two coils with different radii and number of coil windings as the current flowing through the coils is varied. To use the magnetic field strength and current data to experimentally determine the number of turns per unit length of a solenoid coil.

Apparatus and material required: Data collection system, Current sensor, Magnetic field sensor, Sensor extension cable, Primary and Secondary Coil Set, Large base and support rod, Three finger clamp (2), Student power supply (1 A), Patch cord, 4 mm banana plugs, (3)1 (*Note:1The PASPORT Voltage-Current sensor comes with two red 4mm banana plug patch cords) Background Theory: Around 1820 it was shown that two parallel, currentcarrying, wires either attract or repel each other when placed close together. It was then postulated that the repulsive or attractive force experienced by each wire was the result of the electromagnetic fields induced by the charges moving along the length of each wire. It was later shown how the magnetic field induced by a current carrying wire assumes a circular pattern surrounding the wire with directionality perpendicular to the direction of current. The strength of the field was shown to be

Figure 1: Magnetic field lines surrounding a current-carrying

equal to:

wire -------------(1) where is the magnetic field strength in Tesla (T), I is the current through the wire in Amperes (A), r is the perpendicular distance from the wire in meters, and is the permeability of free space constant: 4π × 10-7 T∙m/A. As more current carrying wires (all carrying the same current I) are aligned together, the combined magnetic field of the wires begins to assume a more uniform field.

1

If we take that sheet of wires and bend it into a cylinder we form what is known as a solenoid. If the spacing between the wires in a solenoid is very small, the combined magnetic field inside the solenoid becomes completely uniform, yielding a different equation for its field

Figure 2:

strength

solenoid.

Magnetic field through a current-carrying

-------------(2) where n is the number of wire wraps per unit length of the solenoid. The plot

vs.

, where m =

of equation-2 is a straight line which can be expressed of the form and

-------------(3)

= . Thus we have,

Error Analysis: If

is the error of the number of turns per unit length, then from equation (3) we get: -------------(4)

where

is the error of the slope .

Procedure: Part 1 – Secondary Coil: 1. Mount the magnetic field sensor and secondary coil (red coil windings) to the large base and support rod using the three-finger clamps. 2. Connect the current sensor and the magnetic field sensor to the data collection system. Use the sensor extension cable to connect the magnetic field sensor. 3. Display a graph with Axial Magnetic Field Strength on the y-axis and Current on the x-axis. 4. Drag and drop a digital display for the current and Magnetic Field Strength values. Next Increase the number of decimal places for the Magnetic Field Strength values. 5. Connect the positive and negative terminals from the power supply to 2

Figure 3: Magnetic field sensor and secondary coil setup

the secondary coil through the current sensor. Be certain that the current sensor is connected in series and the negative terminal of the power supply is connected to the top terminal on the coil. 6. Loosen the three-finger clamp and lower the magnetic field sensor into the barrel of the coil. Lower the sensor so the tip is approximately in the middle of the coil, half-way down its length. Keep the orientation of the sensor parallel to the length of the coil. 7. Before turning the power supply on, turn the voltage control knob all the way up (clockwise), and the current control knob all the way down (counterclockwise). 8. Switch the power supply on and make certain the current reading is zero. If the reading is not zero, turn the current control knob on the power supply all the way down (counterclockwise). 9. Begin data recording.

Fig4: Power supply/current sensor

10. SLOWLY turn the current control knob clockwise to increase the current through the coil.

setup

Note: The current control knob on the power supply will adjust the current quickly, so you must turn the knob slowly to avoid missing data points between 0 and 0.25 A. 11. When the current value displayed on the power supply reads approximately 0.25 A, stop increasing the current. 12. Stop data recording. 13. In the Pasco Software Display the run of data in the graph of axial magnetic field strength versus current and adjust the scale of the graph to see the data. 14. Turn the current control knob on the power supply all the way down (counterclockwise) and switch off the power supply. Table-1 (secondary coil) 15. Apply a line of best fit to the run of data in your graph and Current, I (A) Magnetic determine the equation for the line. Record the results as: Field, B (T) Best fit line equation (secondary coil): _____________________________ 16. Turn the current control knob on the power supply all the way down (counterclockwise) and switch on the power supply. 17. Begin data recording. 18. SLOWLY turn the current control knob clockwise to increase the current through the coil and when the current is 0.05 A record the current and the Magnetic Field in Table such as Table-1. Note: The current control knob on the power supply will adjust the current quickly, so you must turn the knob slowly. 19. Repeat a similar procedure such as in step 17 while increasing the current by steps of 0.05 A till you reach 0.25 A while recoding the values in your Table-1. 3

20. When the current value displayed on the power supply reads approximately 0.25 A, stop increasing the current. 21. Stop data recording. 22. Turn the current control knob on the power supply all the way down (counterclockwise) and switch off the power supply. Part 2 – Primary Coil 23. Raise the magnetic field sensor out of the coil and then unhook the leads from the secondary coil and remove it from the three finger clamp. 24. Mount the primary coil (green wire windings) into the three finger clamp with the electrode terminals pointing down. 25. Connect the two loose leads to the terminals on the bottom of the primary coil and lower the magnetic field sensor into the barrel of the coil. Again, lower the sensor so the tip is approximately in the 26. middle of the coil half-way down its length. Keep the orientation of the sensor parallel to the length of the coil. 27. Before turning the power supply on, turn the voltage control knob all the way up (clockwise), and the current control knob all the way down (counterclockwise). 28. Repeat the steps from step 8 to 14 in Part 1 to collect the data. WARNING: Unlike the secondary coil, the primary coil will allow current to flow at greater than 1 A which may damage your current sensor. Do not drive more than 1 A of current though the coil. Note: If you notice that your graph's slope is negative, turn the current control knob the entire way down (counterclockwise), switch off the power supply, and swap the patch cord leads connected to the coil. This will change the direction of current and make the slope positive. Repeat the data collection process for this section.

Figure 4: Magnetic field sensor and primary coil setup

29. Stop increasing the current just before you reach 1 A of current, and then stop data recording. 30. Turn the current control knob on the power supply all the way down (counterclockwise) and switch off the power supply. 31. In the Pasco Software Display the run of data in the graph of axial magnetic field strength versus current and adjust the scale of the graph to see the data. 32. Apply a line of best fit to the run of data in your graph and determine the equation for the line. Record the results as: Best fit line equation (primary coil): _____________________________ 33. Turn the current control knob on the power supply all the way down (counterclockwise) and switch on the power supply. 34. Begin data recording. 4

35. SLOWLY turn the current control knob clockwise to increase the current through the coil and when the current is 0.2 A record the current and the Magnetic Field in Table such as Table-2. Note: The current control knob on the power supply will adjust the current quickly, so you must turn the knob slowly. 36. Repeat a similar procedure such as in step 17 while increasing the current by steps of 0.2 A till you reach 1 A while recoding the values in your Table-2. 37. WARNING: Unlike the secondary coil, the primary coil will allow current to flow at greater than 1 A which may damage your current sensor. Do not drive more than 1 A of current though the coil. Note: If you notice that your graph's slope is negative, turn the current control knob the entire way down (counterclockwise), switch off the power supply, and swap the patch cord leads connected to the coil. This will change the direction of current and make the slope positive. Repeat the data collection process for this section

Table-2 (primary coil) Current, I (A)

Magnetic Field, B (T)

38. When the current value displayed on the power supply reads approximately 1 A, stop increasing the current. 39. Stop data recording. 40. Save your experiment and clean up according to your teacher's instructions. Data Analysis: 1. Using the data from your Table 1 for the secondary coil, plot the graph of Magnetic Field

versus

current . Label the axes and include units on your axes. 2. Draw a line of best fit (straight line) through your graph, and find the slope of the line by choosing two further away points (

) and (

(– )

) as:

( – )

3. Draw a straight line with the least slope possible (minimum best-fit line) and find the slope of it (i.e. minimum slope) and draw a straight line with the greatest slope possible (maximum best-fit line) and find the slope of it (i.e. maximum slope). 4. Using the slopes of these two lines, calculate the final uncertainty in the stated value of the slope m of your best fit line as:

m=

(

)– (

)

5. Using Eq.3 and 4, state the number of turns per unit length of the secondary coil as, :=____________________ 6. Using the data from your Table-2 for repeat a similar procedure (similar to steps 1 to 5 above) for the secondary coil and Using Eq.3 and 4, state the number of turns per unit length of the primary coil as,

:=____________________ 5

Questions: 1. 2.

Briefly explain what a magnetic field is?. Briefly explain what Biot-Savart law states.

*Note: Parts of this lab manual would be based on internationally well-recognized lab manual from PASCO, nevertheless they may have been exclusively edited by adding, removing or modifying, parts to our unique necessities and requirements as appropriate to our labs.

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