General Physics Lab Department of PHYSICS YONSEI University

Lab Manual (Lite)

Magnetic Fields Ver.20181029

Magnetic Fields

Experiment 1. Magnetic Field of a Straight Current-Carrying Conductor (1) Set up your equipment.

Attach the Magnetic Field Sensor to one end of the Rack using the clamp. Insert the other end of the Rack to T-slot on the side of the Rotary Motion Sensor. (The teeth on the Rack go through the T-slot and then engage a pinion gear that is on the shaft of the sensor.)

(2) Set up the PASCO Capstone software. ① Run PASCO Capstone.

② Add the Rotary Motion Sensor. Click [Hardware Setup] in the [Tools] palette. Confirm the panel shows the icon of the Rotary Motion Sensor. (In gen-eral, the interface automatically recognizes the Rotary Motion Sensor.)

NOTICE This LITE version of manual includes only experimental procedures for easier reading on your smartphone. For more information and full instructions of the experiment, see the FULL version of manual.

Procedure

If the sensor is not in the panel, click the input port which you plugged the sensor into. A drop down menu of sensors will appear. Select [Rotary Motion Sensor] from the list and the sensor’s icon will be added to the panel.

③ Add the Magnetic Field Sensor. Click the input port which you plugged the sensor into and

select [Magnetic Field Sensor] from the list.

④ Configure the Rotary Motion Sensor. Click the Rotary Motion Sensor icon in the [Hardware Setup] panel and then click the properties button (☼) in the lower right corner.

In the [Properties] window, select [Rack & Pinion] for [Linear

Accessory]. [Change Sign] switches the sign on the sensor. The sign of collected data depends on the setup status or rotational di-rection of the sensor shaft. Activate [Change Sign] if required. Confirm [Zero Sensor Measurements at Start] is activated. ⑤ Create a graph. Click and drag the [Graph] icon from the [Displays] palette into the workbook page.

A graph display will appear.

⑥ Configure the 𝑥𝑥-axis of the graph. Set up the graph display to show the position of a measuring point on the 𝑥𝑥-axis. Click <Select Measurement> on the vertical axis and pick [Rotary Motion Sensor] [Position(m)] from the menu.

⑦ Configure the 𝑦𝑦-axis of the graph. Set up the graph display to show the magnitude of magnetic

field on the 𝑦𝑦-axis. Click <Select Measurement> on the horizontal axis and pick

[Magnetic Field Sensor] [Magnetic Field Strength (100X)(T)] from the menu.

(3) Set the magnetic field sensor. Orientation : [RADIAL] Range : [100X] (±10−3 T) [TARE] button is for zeroing the sensor.

(4) Supply 𝐼𝐼 = 5 A to the conductor. Before turning on the power supply, rotate the voltage and current adjustment knobs fully counterclockwise for no output settings. Turn on the power supply and rotate the voltage adjustment knob fully clockwise. Then set the current 𝐼𝐼 through the con-ductor at 5 A by using the current adjustment knob.

Note If you cannot obtain the desired output current:

① Check the connections. Make sure the power supply is properly connected to the conductor. ② Check if the CV lamp is on. It indicates that the DC output is in constant voltage mode, i.e. the voltage level you set is too low. Increase the voltage level by rotating the voltage adjustment knob clockwise.

(5) Begin collecting data.

Click the [Record] button at the left end of the [Controls] palette to begin collecting data.

Let the end of the probe touch the conductor (the white dot side of the probe must face up), and then slowly move the sensor away from the conductor, until the end of the probe is separated about 15cm from the conductor.

(6) End the data collection. Click the [Stop] button to end the data collection.

(7) Scale the graph. Adjust the scale of the graph automatically by clicking [Scale axes…] icon in the toolbar.

Note Prior to any measurement, place the Magnetic Field Sensor away from any magnetic sources (current carry-ing conductor, power cables, and even your smartphone) and then press the TARE button on top of the sensor. Pressing the TARE zeroes the sensor at the value of the field it is reading at the moment the button pressed. That means your measurement of the field is not an absolute measurement, but a relative measurement (relative to the value of the field when you press the TARE button). Therefore, pressing the TARE under the influence of any magnetic field might cause spurious results of the exper-iment. For the best result, you should zero the sensor frequent-

ly, every time before each measurement.

Note You can also scale or pan the graph manually.

(8) Analyze the graph. Click [Show coordinates…] to read off data points.

If you want to see more precise values of the collected data, you can use a table display. Drag the [Table] icon into the workbook page, select appropriate measurements for each column, and then increase the number of digits by using the tool-bar icon as shown below.

Note You may get a noisy curve due to the influence of exter-nal magnetic fields, unstable signal of the sensor, or your measurement skills. [Curve Fitting] can be used to find a smooth function that approximately fits the data. ① Click [Select range …] in the toolbar and select a re-gion of interest by resizing the rectangle. (Selected data is highlighted in yellow.)

② Click [▼] of [Select curve fits …] and select the curve fit that you wish to apply to the selected data.

③ The fit function of the data will appear.

(9) Record your data. Find the values of magnetic field 𝐵𝐵 on the graph at the dis-

tance 𝑟𝑟 = 0.01, 0.02, 0.03, 0.04, 0.05 m.

(10) Repeat your experiment. Repeat the steps (5)-(9) more than 5 times. (11) Analyze your results.

𝐵𝐵 =𝜇𝜇0𝐼𝐼2𝜋𝜋𝑟𝑟

(8)

𝑟𝑟 (m) 0.01 0.02 0.03 0.04 0.05

𝐵𝐵 (T)

1st

2nd

3rd

4th

5th

𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

𝐵𝐵𝑡𝑡ℎ𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒 = 𝜇𝜇0𝐼𝐼 2𝜋𝜋𝑟𝑟⁄

Experiment 2. Magnetic Field of a Circular Current Loop (1) Set up the equipment. Mount the circular conductor of radius 𝑎𝑎 = 0.03 m on the base using the Conductor Adapter.

Note The measured value at 𝑥𝑥 = 0 on the graph is NOT the magnetic field strength at 𝑟𝑟 = 0 of 𝐵𝐵 = 𝜇𝜇0𝐼𝐼 2𝜋𝜋𝑟𝑟⁄ . The Hall sensor in the probe is at 8.5mm distance from the center of the conductor when the probe touches the conductor.

This means that the value at 𝑥𝑥 = 0 on the graph is the magnetic field strength at 𝑟𝑟 = 8.5mm distance from the center of the conductor.

(2) Set the Magnetic Field Sensor. Orientation : [AXIAL] Range : [100X] (±10−3 T )

(3) Supply 𝐼𝐼 = 5 A to the conductor. (4) Begin collecting data.

Slowly move the sensor along the axis of the circular con-ductor, keeping the probe parallel to the axis.

(5) Analyze the graph.

Note Prior to any measurement, place the Magnetic Field

Sensor away from any magnetic sources, and then press the TARE button on top of the sensor. For the best result, you should zero the sensor frequently, every time before each measurement.

Note As already explained in previous experiment, [Curve Fitting] can be used to find a smooth function of your data. ① Select [User Defined: f(x)].

② Click the curve fit legend.

③ [Curve Fit Editor] appears in the [Tools] palette.

(6) Record your data. Find the values of magnetic field 𝐵𝐵 on the graph at the

point 𝑥𝑥 = 0.00, 0.01, 0.02, 0.03, 0.04 m. (The maximum value of the graph is the field strength of the conductor center.) (7) Repeat your experiment. Repeat the steps (4)-(5) more than 5 times.

𝐵𝐵𝑥𝑥 =𝜇𝜇0𝐼𝐼𝑎𝑎2

2(𝑥𝑥2 + 𝑎𝑎2)3 2⁄ (12)

𝑥𝑥 (m) 0.00 0.01 0.02 0.03 0.04

𝐵𝐵 (T)

1st

2nd

3rd

4th

5th

𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

𝐵𝐵𝑡𝑡ℎ𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒

(8) Repeat the experiment using the circular conductor of radius 𝑎𝑎 = 0.04 m.

𝐵𝐵𝑥𝑥 =𝜇𝜇0𝐼𝐼𝑎𝑎2

2(𝑥𝑥2 + 𝑎𝑎2)3 2⁄ → 𝑦𝑦 = 𝐴𝐴𝑎𝑎2

((𝑥𝑥 − 𝑥𝑥0)2 + 𝑎𝑎2)3 2⁄ + 𝑦𝑦0

④ Enter your function and click [Apply].

→ y=A*a^2/((x-x0)^2+a^2)^(3/2)+y0

The fit function may not appear at the very moment.

In this case, you need to enter the values in the [Initial

Guess] boxes to modify the function.

1) Click [Lock] check box next to the radius 𝑎𝑎 = 0.03 m

to lock this entry. 2) Enter (𝑥𝑥0,𝑦𝑦0) = (0.06, 0), since the fit 𝑓𝑓(𝑥𝑥 − 𝑥𝑥0) + 𝑦𝑦0 is shifted to the right about (0.06, 0) from 𝑓𝑓(𝑥𝑥), as shown the graph above. (It depends on your data.). 3) You can also enter the calculated value of A = 𝜇𝜇0𝐼𝐼/2. (You don’t have to enter all initial guesses.) 4) Click [Update Fit]. ⑤ The fit function of the data will appear.

Experiment 3. Magnetic field of a solenoid (1) Set up the equipment. We will use the built-in power supply of the interface.

(2) Set up the data acquisition software. ① Add sensors. Add the Rotary Motion Sensor and the Magnetic Field Sen-

sor as explained in previous experiments. In addition, add [Output Voltage Current Sensor] by clicking the output port which you connected the solenoid to.

② Configure a current output. Click [Signal Generator] in the [Tools] palette and select [850 Output 1]. [Waveform] : DC [DC Voltage] : 10V [Auto] automatically starts/stops the signal generator when the interface starts/stops recording data.

③ Create a graph. 𝑥𝑥-axis : [Position(m)] 𝑦𝑦-axis : [Magnetic Field Strength (10X) (T)] ④ Create a digital meter. Create a digital meter to measure the current through the

solenoid. Drag the [Digits] icon from the [Displays] palette into the workbook page, and select [Output Current (A)] for the measurement.

(3) Set the Magnetic Field Sensor. Orientation : [AXIAL] Range : [10X] (±10−2 T ) [TARE] button is used to zero the sensor

(4) Begin collecting data. Put the sensor inside the solenoid and measure the magnet-ic field all over the inside and outside of the solenoid, keeping the sensor probe parallel to the axis of the solenoid.

(5) Analyze the graph. Read the current through the solenoid from the digital meter.

If the graph shows the values of magnetic field as zero, you

can see precise values using a table display. Drag the [Table] icon display into the workbook page, select measurements for each column, and then increase the number of digits by using the icon as shown below.

(6) Record and analyze your results. Repeat the steps (4)-(5) more than 5 times and find the val-

ues of magnetic field 𝐵𝐵 at the center and edge of the sole-noid. (See note of the next page.)

𝐵𝐵 =12 𝜇𝜇0𝑛𝑛𝐼𝐼 �

𝑥𝑥√𝑥𝑥2 + 𝑎𝑎2

+𝐿𝐿 − 𝑥𝑥

�(𝐿𝐿 − 𝑥𝑥)2 + 𝑎𝑎2� (15)

center end

𝐵𝐵 (T)

1st

2nd

3rd

4th

5th

𝐵𝐵𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

𝐵𝐵𝑡𝑡ℎ𝑎𝑎𝑒𝑒𝑎𝑎𝑒𝑒

Please put your equipment in order as shown below. □ Delete your data files from the lab computer. □ Turn off the Computer and the Interface. □ With the voltage and current adjustment knobs set at zero, turn off the power supply and unplug the power cable. □ Handle the solenoid carefully to avoid scratching or stab-bing the coils. □ Do not disassemble the Magnetic Field Sensor assem-bly.

𝐵𝐵 =12𝜇𝜇0𝑛𝑛𝐼𝐼 �

𝑥𝑥√𝑥𝑥2 + 𝑎𝑎2

+𝐿𝐿 − 𝑥𝑥

�(𝐿𝐿 − 𝑥𝑥)2 + 𝑎𝑎2�

→ 𝑦𝑦 = A

⎝

⎛ (𝑥𝑥 − 𝑥𝑥0)

�(𝑥𝑥 − 𝑥𝑥0)2 + 𝑎𝑎2+

𝐿𝐿 − (𝑥𝑥 − 𝑥𝑥0)

��𝐿𝐿 − (𝑥𝑥 − 𝑥𝑥0)�2 + 𝑎𝑎2⎠

⎞ + 𝑦𝑦0

Note Use [Curve Fitting] to find the values of magnetic field at center or at edge of the solenoid. Enter your function and click [Apply].

→ y=A*((x-x0)/((x-x0)^2+a^2)^(1/2)+

(0.13-(x-x0))/((0.13-(x-x0))^2+a^2)^(1/2))+y0

Click [Lock] check box next to the radius 𝑎𝑎 = 0.0195 m

to lock this entry. Enter the calculated value of A = 𝜇𝜇0𝑛𝑛𝐼𝐼/2 if required. The origin of 𝑓𝑓(𝑥𝑥) is on the point O (left end of the so-

lenoid) as shown below.

If you insert the sensor into the right side of the sole-noid, the measuring point of the probe may reach near the center (0.130/2 = 0.065m) of the solenoid. Thus, the fit 𝑓𝑓(𝑥𝑥 − 𝑥𝑥0) + 𝑦𝑦0 is shifted about (−0.065, 0) from 𝑓𝑓(𝑥𝑥). Enter the initial guesses (𝑥𝑥0,𝑦𝑦0) = (−0.065, 0) and Click [Update Fit]. The fit function of the data will appear.

The fit value 𝑥𝑥0 = −0.0692 shows that the point O (left end of the solenoid) is on 𝑥𝑥left = −0.0692 of the graph. (This depends on your result.) Since the length of the solenoid is 𝐿𝐿 = 0.130m, the center of the solenoid is on 𝑥𝑥center = −0.0692 + 0.0650 = −0.0042 and the right edge of the solenoid is on 𝑥𝑥right = −0.0692 + 0.130 =0.0608 of the graph.

End of LAB Checklist