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Florida Atlantic University *

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PHY2049L

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Physics

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Apr 3, 2024

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9

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Experiment 6 - 6.1: Earth's Magnetic Field, 6.2: Magnetic Field of a Solenoid Student name: Juliana Dupuy Pre-lab section: 1) 6.1 Introduction:   Explain the theory behind this experiment in a paragraph between 75 and 150 words . (0.5 points) In this experiment, the oscillation period of a bar magnet in a known field will be measured to determine the horizontal component of the Earth's magnetic field. The time that the bar magnet is suspended to rotate in a specific horizontal plane is known as the oscillation. To create this field, we use two identical Helmholtz coils. A photogate and a PASCO will be used to extract our data measurements: 1/T^2= (m/4Π^2I)x(B) = CB and C=(m/4Π^2I). C depends on magnetic and inertia moment; we get C for the bar magnet   to determine the horizontal component of Earth's field. This helps us to calculate C and magnetic field, Bh, using: 1/T^2 = CBtot = C(Bh + (0.72 Nμ0Ic/R). We plot lines of (1/T^2) and Ic, and   result in a straight slope line with CBh as the intercept. We know that N = 200 turns and R = 10.5 cm, we can determine these numbers. 2) 6.1 Hypothesis:   In an If /Then statement, highlight the purpose of the experiment. (0.5 points) If we collect the PASCO data, the (1/T^2) and Ic of the bar magnet, we can determine the horizontal component of Earth's field by comparing these values to our known field values. 3) 6.2 Introduction:   Explain the theory behind this experiment in a paragraph between 75 and 150 words . (0.5 points) In this experiment, we are going to calculate the magnetic field measurements within a solenoid. The magnetic field within a solenoid can be expressed by the equation:   B= μ0nI. Moreover, I represents the solenoid's current (A), μ0=(4Πx10^-7), and n is the number of wire turns per unit length (#/m) of the solenoid. In addition to using a magnetic field sensor to collect the data and a PASCO interface to receive measurements, we are also using a solenoid as our subject. 4) 6.2 Hypothesis:   In an If /Then statement, highlight the purpose of the experiment. (0.5 points) If the inertia and magnetic field are measured accurately, the magnetic field inside a solenoid can be determined using the slope. Post-lab section: 5) 6.1 Discussion: In a paragraph between 100 and 150 words , explain what you learned from the results obtained in the experiment . What conclusion can you draw from the results of this lab assignment?   (1.0 points) the horizontal component was measured by looking at how the bar was affected in the magnetic field In this experiment, we were able to observe how the bar behaved in the magnetic field, and the horizontal component was calculated. The torque generated by the strength of the magnetic field is what causes the bar movement. The bar magnetic moment and moment of inertia determined the constant C in C=m/4π^2I. Also, the Helmholtz coil, produced the known magnetic field. The coils have the same amount and direction of current in each coil so that the magnetic field will have the same magnitude and direction at the halfway point between both coils. This is determined by the equation B =.72NμoIc/R, in this case, 200R is the radius, .105 meters and I is the current, 4πx10^-7 T(m)/A. The formula for the constant
C and the magnetic field B is CB=CB+C(.72NμoIc)/R. After all the calculations, we got 8% of error. 6) 6.1 Conclusion: In one   sentence,   compare the results of the experiment with your Hypothesis. Why? (0.5 point) The results of the experiment   I   did, helped me figure it out that my   hypothesis   is true. We had (1/T^2) and Ic and we were able to find the horizontal component of Earth's. 7) 6.2 Discussion: In a paragraph between 100 and 150 words , explain what you learned from the results obtained in the experiment . What conclusion can you draw from the results of this lab assignment?   (1.0 points) The magnetic field within a solenoid was measured and expressed as B=μonI, with μo=4πx10^-7, I representing the current flowing through the solenoid, and n the number of wire turns per unit length of the solenoid. Also, it was discovered that the magnetic field's strength grew proportionally to the solenoid's current flow. Table 3 illustrates this, showing how the magnetic field's strength increased as the current increased. This result confirms the relationship between current and magnetic field strength in a solenoid and is consistent with the theoretical understanding of electromagnetic. In overall, the experiment demonstrated the importance of coil configuration in affecting magnetic field characteristics and taught us the direct correlation between current and magnetic field intensity in a solenoid. The experiment in value was 26021 while the given n value is 29795.9, the percentage error is that of 14.5%. The experiment in value was 26021 while the given n value
is 29795.9, the percentage error is that of 14.5% 8) 6.2 Conclusion: In one   sentence,   compare the results of the experiment with your Hypothesis. Why? (0.5 point) The results of the experiment showed that my hypothesis was true, we can see that in table 3 the value of B(theory) increased as the current increased. 9) 6.1 Data Analysis: Attach an image of the data and instruction pages containing tables with final calculated values, figures, plots, charts and responses to questions or specified calculations here. (5 points) Table 1: 2 points Current I (A) Period T (s) 1/T^2 (s^-2) -0.002 2.542 0.1547565 0.018 1.752 0.032578553 0.037 1.363 0.53828006 0.056 1.165 0.73679651 0.076 1.031 0.94076829 0.096 0.937 1.13899238 0.116 0.862 1.34581532 0.135 0.805 1.54315034 0.156 0.757 1.74505147 0.175 0.716 1.95062576 Table 2: 2 points Slope Intercept C B h (exp.) B h (literature) in south Florida % error 10.2 0.162 5960 0.27 0.25 8.0 Image of excel plot and data table for table 1 **Include excel file in the comment area of the assignment (3 points deduction)
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 I vs 1/T^2 Output Current (A) Calculation 1 ( 1/T^2) -0.05 0 0.05 0.1 0.15 0.2 -0.05 0 0.05 0.1 0.15 0.2 Series2 10) 6.1 Calculations: Attach an image all your calculation pages here . (2 points)
Calculation for ‘C’ and ‘B h ’ values for Table 2. (1 point) Calculate the % error between B h (exp.) and B h (literature) for table 2 (1 point) 11) 6.1 End of Experiment Questions: Attach an image of the lab manual pages containing your responses to the end of experiment questions here. (1.75 points) Question 1: 0.25 point Question 2: 0.25 point Question 3: 1.0 point
Question 4: 0.5 point (extra credit) Question 5: 0.25 point
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12) 6.2 Data Analysis: Attach an image of the data and instruction pages containing tables with final calculated values, figures, plots, charts and responses to questions or specified calculations here. (4 points) This should include: Table 3 Current I ( A ) B(exp.) (Gauss) B(theory) (Gauss) 0.010 4.20 3.74 0.024 8.51 8.98 0.036 12.88 13.5 0.050 17.09 18.7 0.063 21.54 23.6 0.076 26.07 28.4 0.089 30.36 33.3 0.102 34.51 38.2 0.115 38.80 43 0.128 42.23 47.9 0.141 47.49 52.8 0.154 51.85 57.6 0.168 56.19 62.9 0.181 60.42 67.7 0.194 64.52 72.6 Slope of I vs b (exp 329.6593142 Table 4 Question g Slope of I vs B(exp.) plot n(exp.) n(given) used in calc. of % error
B(theory) 330 33400 29800 12.0 Image of excel plot and data table for table 1 **Include excel file in the comment area of the assignment (3 points deduction) 0.000 0.050 0.100 0.150 0.200 0.250 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 Current I (A) and B exp appear highly correlated B exp Linear (B exp ) Current I (A) B exp 0.000 0.050 0.100 0.150 0.200 0.250 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 Current I (A) and B Theory appear highly correlated B theory Linear (B theory) Current I (A) B Theory 13) 6.2 Calculations: Attach an image all your calculation pages here . (1.0 point)
14) 6.2 End of Experiment Questions: Attach an image of the lab manual pages containing your responses to the end of experiment questions here. (1.25 points) This should include: Question 1: 0.25 point Question 2: 1.0 point
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