Practice Problem 21.09 - Enhanced - with Feedback SET UP AND SOLVE At time t = 3.0 us, the current in coil 2 is 12 = (2.0 x 105 A/s)(3.0 x 10-6 s) = 6.0 A. A Tesla coil is a type of high-voltage generator that was invented by Nikola To find the flux in the solenoid, we need to know the mutual inductance of the coils. Tesla (1856-1943). In one form of Tesla coil, shown in (Figure 1), a long solenoid with length / and cross-sectional area A is closely wound with N1 M = HANIN2 (47 x10-7 Wb/(A.m))(10x10-4 m?)(1000) (10) turns of wire. A coil with N2 turns surrounds it at its center. You have a Tesla 1 0.50 m coil with 1 = 0.50 m, A = 10 cm, N1 = 1000 turns, and N2 = 10 turns. = 2.5 X 10 - H. Let's apply a time-varying current to the blue coil. Suppose the current i2 is given by i2 = (2.0 x 10 A/s)t. At time t = 3.0 us, what is the average Now we can solve Ni|DB1 | = M|i2 | for the average magnetic flux in coil 1: magnetic flux through each turn of the solenoid caused by the current in the smaller coil? What is the induced emf in the solenoid? 1($ B1 )avg| = Mlizl (2.5x10 5 H)(6.0 A) N1 1000 = 1.5 x 10-7 Wb. This is an average value; the flux will vary considerably from the center to the ends. The induced emf, E1, is given by & = [MAi2/ At with the change in current per unit time, Ai2/At, equal to 2.0 x 106 A/s: 81 = MAi2 = (2.5 x 10-5 H)(2.0 x 106 A/s) = 50 V. REFLECT In an operating Tesla coil, Ai2/ At would be alternating much more rapidly, and its magnitude would be much larger than in this example. Part A - Practice Problem: For the given Tesla coil, how many turns (N1) should coil 1 have in order to get an induced emf magnitude of 390 V? Figure Express your answer as a number of turns. IVE AEd ? Cross-sectional area A M1= 7100 turns Submit Previous Answers Request Answer X Incorrect; Try Again; 6 attempts remaining Blue coil: N2 turns Black coil: N turns Provide Feedback