DATA As a summer intern at a research lab, you are given a long solenoid that has tw...

DATA As a summer intern at a research lab, you are given a long solenoid that has two separate windings that are wound close together, in the same direction, on the same hollow cylindrical form. You must determine the number of turns in each winding. The solenoid has length L = 40.0 cm and diameter 2.80 cm. You let a 2.00-mA current flow in winding 1 and vary the current I in winding 2; both currents flow in the same direction. Then you measure the magnetic-field magnitude B at the center of the solenoid as a function of I. You plot your results as BL/µ₀ versus I. The graph in Fig. P28.76 shows the best-fit straight line to your data. (a) Explain why the data plotted in this way should fall close to a straight line. (b) Use Fig. P28.76 to calculate N₁ and N₂, the number of turns in windings 1 and 2. (c) If the current in winding 1 remains 2.00 mA in its original direction and winding 2 has I = 5.00 mA in the opposite direction, what is B at the center of the solenoid?