Lab Assignment: Determining the relationship between current and magnetic field Part 4: Magnetic field due to current through a solenoid varying the number of coils You have a solenoid, through which you are running a constant DC current, but you neglected to record the current in the solenoid. Our goal in this part is to use a graph of this data in order to determine the current, if the length of the solenoid was 0.04 m. We will look at the data taken in the lab. For this part of the lab, you and your partner recorded the following data: N Magnetic field (mT) 200 0.116238 400 0.232477 800 0.464955 3200 1.859822 28. Create a graph of the magnetic field vs. number of coils, where the independent variable (number of coils) is on the x-axis and the dependent variable (magnetic field) is on the y-axis. Insert an appropriate trendline and display its equation, and then paste the image of your graph below. Magnetic Field vs. Number of Coils 2 18 y = 0.0006x - 8E-07 e - 16 - o 14 12 1 o 0.8 206 04 o 02 o 0 0 500 1000 1500 2000 2500 3000 3500 netic fiel 3y Number of Coils 29. Is the graph linear? Based on the formula for magnetic field and number of coils, should it be linear? * Yes, The graph is linear * Based on the formula for magnelic field and number of coils, if should be linear 30. Insert the equation for the line in your graph, and record the slope of your graph here. 4 = 0.0006x -(8x107) m = 0.0006 31. Now compare the equation for magnetic field to that slope of the linear graph. What formula do you have for slope? 32. Set the slope of the line equal to the formula you just determined. Then solve for the current in the solenoid. Show your work. (Hint: convert the magnetic field to Tesla from milliTesla before doing the math.) 10 Lab Assignment: Determining the relationship between current and magnetic field Part 3: Magnetic field due to current through a solenoid varying the current You have a solenoid, through which you are running a constant DC current, but you neglected to record the number of coils in the solenoid. Our goal in this part is to use a graph of this data in order to determine the number of coils, if the length of the solenoid was 0.04 m. 19. What is the theoretical formula for the magnetic field created by a current running through a solenoid? B :_'U'MI L 20. What should the graph of magnetic field vs current look like? Circle the appropriate shape. For the graphs, remember that graphing conventions are that the independent variable is graphed on the x-axis, and the dependent variable is graphed on the y-axis. 0.000007 0.000007 0.000006 * 0.000006 | et o 0.000005 0000005 | | et 0.000004 0.000004 0.000003 . 0.000003 . 0.000002 "--..' 0.000002 o' 0.000001 O 9. ig...g 0.000001 l. 0 0 0.00 100.00 200.00 300.00 400.00 500.00 0.000007 0.000006 - 0.000005 ; 0.000004 - 0.000003 e 0.000002 o o 0.000001 P 0 0.00 5.00 10.00 15.00 20.00 25.0( Lab Assignment: Determining the relationship between current and magnetic field Next, we will look at the data taken in the lab. For this part of the lab, you and your partner recorded the following data: current (A) B (mT) 0.0185 1.85982285 0.00917 0.92186895 0.02824 2.83899445 0.03733 3.75282092 21.Create a graph of the magnetic field vs. current, where the independent variable (current) is on the x-axis and the dependent variable (magnetic field) is on the y-axis. Insert an appropriate trendline and display its equation, and then paste the image of your graph below. Magnetic Field vs. Current - .9 35 y =100.53x ; w Magnetic Field o - ~ o w _ w N w o o 8 o 2 o 2 o o 8 o o S o o 2 o o 2 o o g Current 22. Is the graph linear? Based on the formula for magnetic field and current, should it be linear? * Yes, the graph is linear * Based on the formula for magnetic field and current, it should be linear 23. Now create a graph of the magnetic field vs. the inverse of the current, where the independent variable (1/current) is on the x-axis and the dependent variable (magnetic field) is on the y-axis. Insert an appropriate trendline and display its equation, and then paste the image of your graph below. Magnetic Field vs. Inverse Current Magnetic Field = ~N w N U w - o i m n y =100.53x! Inverse Current Lab Assignment: Determining the relationship between current and magnetic field 24. Is the graph linear? Based on the formula for magnetic field and current, should it be linear? * The graph is not linear, but it is a power graph * Based on the formula for magnetic field and current, it should be linear 25. For the two graphs above, one of them should be linear, and one will not be. Using the graph that is linear, use Excel and find the slope of the line. Record that slope here. m - 40053 - # 26. Now compare the equation for magnetic field to that slope of the linear graph. What formula do you have for slope? 27. Set the slope of the line equal to the formula you just determined. Then solve for the number of loops in the solenoid. Show your work. (Hint: convert the magnetic field to Tesla from milliTesla before doing the math.)