SOLUTION Practice Problem 21.9 SET UP AND SOLVE At time t 3.0s, the current in c
ID: 1774848 • Letter: S
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SOLUTION Practice Problem 21.9 SET UP AND SOLVE At time t 3.0s, the current in coil 2 is (2.0 × 106A/s)(3.0 × 10-6s) = 6.0A A Tesla coil is a type of high-voltage generator that was invented by Nikola Tesla (1856-1943). In one form of Tesla coil, shown in (Figure 1), a long solenoid with length 1 and cross-sectional area A is closely wound with Ni turns of wire. A coil with N2 turns surrounds it at its center. You have a Tesla coil with 1 0.50m . A 10cm 2 N, 1000 turns, and N2-10 turns. Let's apply a time-varying current to the blue coil Suppose the current 22 is given by 12 (2.0 × 106 A/s)t. At time 3.0s, what is the average magnetic flux through each turn of the solenoid caused by the current in the smaller coil? What is the induced emf in the solenoid? 12 To find the flux in the solenoid, we need to know the mutual inductance of the coils (4×10-7 wb/(A-m))(10x10-4m2)(1000)(10) 0.50m HyAN,N, = 2.5 × 10-5H Now we can solve Ni B1-Mi2l for the average magnetic flux in coil 1 Mligl _ (2.5x10+D(6.0A) = 1.5 x 10-7Wh 1000 This is an average value; the flux will vary considerably from the center to the ends The induced emf, 1 , is given by = lM'2/Atl with the change in current per unit time, 12/At equal to 2.0x106 A/s €1 = M .| = (2.5 × 10-5 H)(2.0 × 106A/s) 50V REFLECT in an operating Tesla coil, 22/t would be alternating much more rapidly, and its magnitude would be much larger than in this example Figure 1 of 1 Part A - Practice Problem: Cross-sectional area A For the given Tesla coil, how many turns (N1) should coil 1 have in order to get an induced emf magnitude of 695 V ? Express your answer in turns to two significant figures Blue coil: N2 turns Black coil: Ni turns turnsExplanation / Answer
emf induced in the coil
e = M di2 / dt
M = 695 / (2 x106 ) = 347x10-6
Number of turns
N1 = (347x10-6) ( 6A) / (1.5x10-7 ) = 13900 turns
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