This Is a lab Manual That you can use to answer the questions. I'm really confused about the questions I would really appreciate it if you can help I have an exam on this lab so I need correct answers for the questions.

Introduction In this lab we will study the magnetic field due to a current- carrying circular loop Figure 1 using the Biot-Savart law. The Biot-Savart Law states the relationship between the magnetic field contribution dB and its source current element dL (small segment of length dl of the wire forming the loop), carrying a steady current / which is given by dB = Home [d[ x # ] (1) where #, = 4x x 10 7 T.m/A is the permeability of free space, r and f are the distance from the current to the field point and the corresponding unit vector along r, respectively (see Figure 1). By integrating Eq. (1) it can be proven that the strength of the magnetic field at the center of a current- carrying coil depends on the coil current /and radius Ras Beall = Ho 2R 1 1 If the circular coil consists of N turns, then Bcoll = HO 2R NI (2) In the first part of this lab you will test Eq. (2) by measuring the magnetic Figure 2 field at the center of a current carrying circular coil as a function of current. If your experimental data support the Biot-Savart law, the magnetic field must linearly depend on the current and the permeability of free space which can be determined from the slope of the Bean vs / graph. Where the value of Ho you find should be close to its acceptable value within experimental error. In the second part of the lab, you will use the Biot-Savart law to measure the strength of some unknown magnetic field Bunknown (if there is one) located within the center of the current-currying coil, the horizontal component of the Earth's magnetic field, for example. To do that, you will "build" a tangent galvanometer consisting of a large circular coil (the same coil as used in the first part of the lab) and a3. Earth's Magnetic Field The Earth's magnetic field can be represented by three components: X (pointing to North), Y (pointing to East) and Z (pointing Down towards the center of the Earth). A typical procedure for measuring its direction is to use a compass to determine the direction of magnetic North. The angle between magnetic north and true north is called magnetic declination (D), while the angle the Earth's magnetic field makes with the horizontal is called magnetic inclination (1) or magnetic dip. In the second part of the lab you will measure the horizontal component of the Earth's magnetic field, Bxy,Earth. Give your best estimate for the Earth's magnetic field strength you expect to get in your measurements including an estimate of the uncertainty for this value. Model Used: WMM-2020 Chicago, IL Latitude: 410 52' 59" N Longitude: 870 39' 31" W Elevation: 0.0 km Mean Sea Level Date Declination Inclination North Comp East Comp Vertical Comp Total Field ( +E I - W) ( + D I - U ) (+ N 1 - S) (+ E 1 - W) ( + D I - U) 2022-02-16 -40 1' 50" 580 45' 22" 19,245.2 nT 1,356.0 nT 49,627.5 nT 53,245.7 nT Change/year -00 2' 37"/yr -00 4' 59"/yr 32.8 nT/yr 17.0 nT/yr 125.6 nT/yr -104.8 nT/yr Uncertainty 00 23' 00 13 131 nT 94 nT 157 nT 145 nT Show your work. Bxy,Earth nT 4. The coil is alligned along a north south line as shown in the figure to the right Top View IN and is carrying a current of 10 mA. If you will place a magnetic needle at the center Coil of the coil, at what angle 0 (in degrees) with respect to the vertical will the needle point? Show your work. Magnetic arrow S 0 =Part 2: The Earth's Magnetic Field Let's apply the BiotSavart law to determine the strength of the Earth's Figure 3 magnetic eld at your current location. 2.1. Re-assemble the equipment as shown in Figure 3: I Remove Sensor Assembly from the Straight Track and place it on top of the Power Supply I Unplug the red and black terminals from the Power Supply and reattach the red terminal into the right-hand side output connector (~) on Pasco Interface and black terminal into the left-hand side output connector (4-). I Detach the Straight Track and place it on the Table I Re-attach Coil #1 to Table using hole 2 align its base to y0 y0 with I connectors on base facing towards the Power Supply. Dan'tforget toput the washer between 60175 base and Table I Re-attach the Straight Track to the Table using leg 1 in hole 17 and leg 2 in hole 18 Table 2 I Place a wooden base at the center of 6' I 3 Track and carefully put the compass on tan 6' 6\" . degree A pT top of It 20 2.2. Delete \"Graph\" display from the Capstone's window and move "Digits\" display near the right 30 corner of the window. 40 2.3. Click "Signal Generator\" on left-hand \"Tools Menu\To do so, click "Data Summary\" icon on left side menu, then under "Magnetic Field Sensor Ch A\" click \"Magnetic Field Strength (1X) (T), and then click on "Properties\" icon. Click on "Numerical Format\" and make the following changes: 0 Number Style to Scientic Notation 0 Number of Signicant Figures to 3 Now, you can close the "Data Summary\" window by clicking on its icon. I Drag a \"Digits\" display icon to the central page, then click and choose "Current (A)\" I Change the number style to "Scientic Notation\" with 3 signicant gures To do so, position the mouse pointer within the \"Digits\" display, click on the gear icon. Click on \"Numerical Format\" and make the following changes: 0 Number Style to Scientic Notation 0 Number of Signicant Figures to 3 1.4. Use the brass thumbscrew with the washer between the coil base and Table to attach Coil #1 to Table using hole 5. Then, align the coil base to KS x5 with connectors on base facing towards you. 1.5. Take the Straight Track and thread it through Coil and then insert Straight Track leg L1 into hole 8 and leg L2 into hole 7. 1.6. To wire the circuit, I Plug one end of the red cable into the Power Supply's red connector and the other end into the Current Sensor's red terminal I Plug one end of green cable into the Current Sensor's black terminal and other end into the white center connector at the base of Coil #1. I Plug one end of the black cable into the left most white connector at the base of Coil #1 base and the other end into the Power Supply's black connector. Experimental Procedure In this experiment you will measure the magnetic eld at the center of a current carrying circular coil as a function of current. If your data support the BiotSavart law, then the slope of the flex].p vs I graph must be simply no % within experimental error. Let's verify it. 1.7. Place Sensor Assembly (Cart with attached Magnetic Field Sensor) on Straight Track and align axle of Sensor Assembly with 0 cm mark on Track's scale. Then, gently depress the "Tare\" button on top of the magnetic eld sensor. 1.8. Turn both "Coarse\" and "Fine\" Voltage knobs all way counterclockwise, and both \"Coarse\" and "Fine\" Current knobs all way clockwise. Turn Power Supply 0N. 1.9. Slowly turn "Coarse\" Voltage knob clockwise until the Power Supply's voltmeter shows 5.0 V. 1.10. Click "Record\Part 1: Magnetic Field at the Center of a Circular Current-Carrying Coll Before you begin the initial setup of the rst experiment, we must measure the coil. 1.1. Select Coil #1 and measure its inner radius Rim,\" and outer radius Rim\1. A circular coil of radius R has N turns and is carrying current I. Use Eq. (1) in the lab manual to derive the expression for the strength of the magnetic eld at the center of the coil. Show your work. 2. The coil used in the lab has 300 turns and its radius is 10.5 cm. If it's carrying current of 0.5 A, what is the magnitude of the magnetic eld at the center of the coil? Show your work 1.12. Go to the graph toolbar and click "Data Highlighter\" :2/ , then Table 1 I Resize the high-lighter rectangle. I Drag the highlighter over the data at the beginning of the B vs time graph (nearly at segment), then click \"Statistics\" icon I to nd the average background level of magnetic eld strength 30 and record its value in Table 1. I Repeat it for the maximum strength of magnetic eld 3mm: and record 3_0 its value in Table 1 I Calculate the strength of magnetic 2-5 eld Hex.p = Bmax Bo and record 10 its value in Table 1 1.13. Reduce the voltage to the next value listed in Table 1 and repeat 1.10 and 1.12 steps. 1.14. When you are done with Table 1, turn the \"Coarse\" Voltage knobs all way counterclockwise and turn OFF the Power Supply. 1.15. Plot Ben, vs I graph and nd the slope and y-intercept. You can use LINESTO function to nd the slope, intercept, its uncertainties and the coefcient of determination. Record its values below. Slope = i TIA Intercept = i T R2 = 1.16. Does your result agree with the prediction of Eq. (2)? Explain your reasoning. 1.17. Determine the permeability of free space, #0, by using your experimental results above. Apply error propagation to estimate the error associated with your experimental value of #o- What is the precision of your measurements of the #0? Determine the accuracy of your measurements. Show your work. \"0.9m = :l: \"T . m/A Note: Accepted value for no is 1.26 pT - m/A. magnetized floating needle (compass) at its center (see Figure 2) with the graduated dial from 0 to 360 degrees on the circumference of the housing. If the coil of the tangent galvanometer is aligned with the unknown magnetic field and the current is on, the two magnetic fields will add to give a resultant field. The needle of the tangent galvanometer will line- up with this resultant magnetic field. The deflection angle 0 can be measured and the magnetic field Bunknown can be calculated from the right triangle shown in Figure 2. In this part of the lab, you will determine the strength of the magnetic field at the center of the coil which is not due to the current in the coil. In the absence of significant magnetic fields around in the lab room, this unknown magnetic field, you will try to measure, should have the magnitude that is quite close to the horizontal component of the magnetic field of the Earth. Equipment Pasco interface 750 DC power supply Pasco magnetic field sensor attached to cart Current sensor 46" red, black and green cables Gray PVC Table with accessories Straight Track Pasco coil equipped with brass thumb screw and flat 1" in diameter washer Compass Wooden base2.9. Plot Bcou VS. tan 0 graph and find the slope and y-intercept. You can use LINEST() function to find the slope, intercept and its uncertainties. Record the results below. Slope (B Earth,exp ) = HT Intercept = HT R2 = The strength of the horizontal component of the Earth magnetic field in Chicago, Bxy,Earth = (19.24 + 0.13) HT Source: https://www.ngdc.noaa.gov/geomag/calculators/magcalc.shtml#igrfwmm 2.10. Does your result agree with the accepted value for the strength of the Earth's magnetic field in Chicago? Briefly explain your answer. 2.11. What is the precision of your measurements of the Earth's horizontal component of magnetic field? Determine the accuracy of your measurements. Is there an indication of systematic error in your measurements? If so, what is the main source of the error