Magnetic Fields. Experiment 1. Magnetic Field of a Straight Current-Carrying Conductor

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1 General Physics Lab Department of PHYSICS YONSEI University Lab Manual (Lite) Magnetic Fields Ver 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. Magnetic Fields Procedure 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 general, the interface automatically recognizes the Rotary Motion Sensor.)

2 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 direction 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.

3 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 conductor at 5 A by using the current adjustment knob. 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.

4 (5) Begin collecting data. Prior to any measurement, place the Magnetic Field Sensor away from any magnetic sources (current carrying 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 experiment. For the best result, you should zero the sensor frequently, every time before each measurement. 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. You can also scale or pan the graph manually.

5 (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. You may get a noisy curve due to the influence of external 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 region 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.

6 (9) Record your data. Find the values of magnetic field BB on the graph at the distance rr = 0.01, 0.02, 0.03, 0.04, 0.05 m. The measured value at xx = 0 on the graph is NOT the magnetic field strength at rr = 0 of BB = μμ 0 II 2ππππ. 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. (10) Repeat your experiment. Repeat the steps (5)-(9) more than 5 times. (11) Analyze your results. BB = μμ 0II 2ππππ (8) rr (m) st 2nd BB (T) 3rd 4th 5th BB aaaaaaaaaaaaaa BB ttheeeeeeee = μμ 0 II 2ππππ 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.

7 (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. 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. Slowly move the sensor along the axis of the circular conductor, keeping the probe parallel to the axis. (5) Analyze the graph. 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.

8 4 Enter your function and click [Apply]. μμ 0 IIaa 2 BB xx = 2(xx 2 + aa 2 ) 3 2 yy = AA aa 2 ((xx xx 0 ) 2 + aa 2 ) yy 0 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 (xx 0, yy 0 ) = (0.06, 0), since the fit ff(xx xx 0 ) + yy 0 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 = μμ 0 II/2. (You don t have to enter all initial guesses.) 4) Click [Update Fit]. 5 The fit function of the data will appear. (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. μμ 0 IIaa 2 BB xx = 2(xx 2 + aa 2 ) 3 (12) 2 xx (m) st 2nd BB (T) 3rd 4th 5th BB aaaaaaaaaaaaaa BB ttheeeeeeee (8) Repeat the experiment using the circular conductor of radius aa = 0.04 m.

9 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 Sensor 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.

10 (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 magnetic 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 values of magnetic field BB at the center and edge of the solenoid. (See note of the next page.) BB = 1 2 μμ xx 0nnnn xx 2 + aa + LL xx 2 (15) (LL xx) 2 + aa2 center end 1st 2nd BB (T) 3rd 4th 5th BB aaaaaaaaaaaaaa BB ttheeeeeeee

11 Use [Curve Fitting] to find the values of magnetic field at center or at edge of the solenoid. Enter your function and click [Apply]. BB = 1 2 μμ xx 0nnnn xx 2 + aa + LL xx 2 (LL xx) 2 + aa 2 (xx xx yy = A 0 ) (xx xx 0 ) 2 + aa + LL (xx xx 0 ) + yy 0 2 LL (xx xx 0 ) 2 + aa 2 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 = m to lock this entry. Enter the calculated value of A = μμ 0 nnnn/2 if required. The origin of ff(xx) is on the point O (left end of the solenoid) as shown below. If you insert the sensor into the right side of the solenoid, the measuring point of the probe may reach near the center (0.130/2 = 0.065m) of the solenoid. Thus, the fit ff(xx xx 0 ) + yy 0 is shifted about ( 0.065, 0) from ff(xx). Enter the initial guesses (xx 0, yy 0 ) = ( 0.065, 0) and Click [Update Fit]. The fit function of the data will appear. The fit value xx 0 = shows that the point O (left end of the solenoid) is on xx left = 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 xx center = = and the right edge of the solenoid is on xx right = = of the graph. End of LAB Checklist 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 stabbing the coils. Do not disassemble the Magnetic Field Sensor assembly.

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