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Activity 17.3 Dependence of a Dipole's B-field on Distance Magnetic B North North BE W- E mappers BM (smal compesses) Figure 6 Figure 7 For a dipole oriented as in Figure 6, the B-field it generates at positions along cither axis will be only in the +x or-x direction. The ambient Bg, on the other hand, has only a Y component, since you oriented the paper that way. Figure 7 shows the Bmet for some position on the X-axis and we can

Activity 17.3 Dependence of a Dipole's B-field on Distance Magnetic B North North BE W- E mappers BM (smal compesses) Figure 6 Figure 7 For a dipole oriented as in Figure 6, the B-field it generates at positions along cither axis will be only in the +x or-x direction. The ambient Bg, on the other hand, has only a Y component, since you oriented the paper that way. Figure 7 shows the Bmet for some position on the X-axis and we can

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Activity 17.3 Dependence of a Dipole's B-field on Distance Magnetic North North BE W-O mappers Вм (smal compasses) Figure 6 Figure 7 For a dipole oriented as in Figure 6, the B-field it generates at positions along cither axis will be only in the +x or -x direction. The ambient Bg, on the other hand, has only a Y component, since you oriented the paper that way. Figure 7 shows the Bnet for some position on the X-axis and we can write: tan e (angle from North) = M or By = Bg tan e. Thus, we can determine By as a function of x (distance along the X-axis) by measuring e for difference values of x. What kind of power law would you expect based upon your experience with electricity and gravity? 108 x (cm) 10 13 16 19 40 43 46 Figure 8 In Excel, create a spreadsheet with the following cight columns: x (cm), 8 (deg), AB(deg), 8 (rad), e + A8 (rad), By = Bg tan e (G), BM,max = Bg tan( + A8) (G), and AB = BM max - BM. Use BE = BEhorizontal = 0,21 G from the table above.
Transcribed Image Text:Activity 17.3 Dependence of a Dipole's B-field on Distance Magnetic North North BE W-O mappers Вм (smal compasses) Figure 6 Figure 7 For a dipole oriented as in Figure 6, the B-field it generates at positions along cither axis will be only in the +x or -x direction. The ambient Bg, on the other hand, has only a Y component, since you oriented the paper that way. Figure 7 shows the Bnet for some position on the X-axis and we can write: tan e (angle from North) = M or By = Bg tan e. Thus, we can determine By as a function of x (distance along the X-axis) by measuring e for difference values of x. What kind of power law would you expect based upon your experience with electricity and gravity? 108 x (cm) 10 13 16 19 40 43 46 Figure 8 In Excel, create a spreadsheet with the following cight columns: x (cm), 8 (deg), AB(deg), 8 (rad), e + A8 (rad), By = Bg tan e (G), BM,max = Bg tan( + A8) (G), and AB = BM max - BM. Use BE = BEhorizontal = 0,21 G from the table above.
1. Along the +X axis, record the angular deflection 0 of the mapper as a function of x for at least 10 points. Sec Figure 8. Note: Take 8 with respect to magnetic N. not "E"! Devise a way of extending the needle's direction so you can measure the angle (the mapper's angular markings are quite small). Use your own judgement as to how close to the magnet will still give you reliable readings. Which data points have the greatest uncertainty? Consider tan(89° t 0.5) versus tan(50° + 0.5)! 10 13 Figure 9 16 2. Plot the data with error bars and power law trendline: a. Plot the Data i. Left-click "x" column ii. Ctrl-left-click "BM" column iii. "Insert" "Scatter" b. Display Error Bars (Vertical Only) i. Select Chart and select "Chart Elements" ii. "Error Bars" "More Options..." iii. Direction: "Both" iv. Error Amount: "Custom" "Specify Value" v. Select ABM column for both positive and negative error values vi. Select and delete horizontal error bars c. Display Trendline Equation i. "Chart Elements" - "Trendline" - "More Options..." ii. In the Trendline Options panel, select "Power" iii. Check "Display Equation on Chart" and reposition on chart as needed 109 3. Submit a graph of B (Gauss) vs. x (cm), along with data and calculations. If a few data points (those for small distances) are so far out on the plot that all the other points are compressed close to the origin, ignore these few as you plot again. 4. Fold and submit your B-field plot (to be graded on accuracy, completeness, and neatness).
Transcribed Image Text:1. Along the +X axis, record the angular deflection 0 of the mapper as a function of x for at least 10 points. Sec Figure 8. Note: Take 8 with respect to magnetic N. not "E"! Devise a way of extending the needle's direction so you can measure the angle (the mapper's angular markings are quite small). Use your own judgement as to how close to the magnet will still give you reliable readings. Which data points have the greatest uncertainty? Consider tan(89° t 0.5) versus tan(50° + 0.5)! 10 13 Figure 9 16 2. Plot the data with error bars and power law trendline: a. Plot the Data i. Left-click "x" column ii. Ctrl-left-click "BM" column iii. "Insert" "Scatter" b. Display Error Bars (Vertical Only) i. Select Chart and select "Chart Elements" ii. "Error Bars" "More Options..." iii. Direction: "Both" iv. Error Amount: "Custom" "Specify Value" v. Select ABM column for both positive and negative error values vi. Select and delete horizontal error bars c. Display Trendline Equation i. "Chart Elements" - "Trendline" - "More Options..." ii. In the Trendline Options panel, select "Power" iii. Check "Display Equation on Chart" and reposition on chart as needed 109 3. Submit a graph of B (Gauss) vs. x (cm), along with data and calculations. If a few data points (those for small distances) are so far out on the plot that all the other points are compressed close to the origin, ignore these few as you plot again. 4. Fold and submit your B-field plot (to be graded on accuracy, completeness, and neatness).
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