普通物理 General Physics 30 - Inductance 郭艷光 Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件：ykuo@cc.ncue.edu.tw 網頁：http://ykuo.ncue.edu.tw

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Outline 30-1 What Is Physics? 30-2 Two Experiments 30-3 Faraday’s Law of Induction 30-4 Lenz’s Law 30-5 Induction and Energy Transfers 30-6 Induced Electric Fields 30-7 Inductors and Inductance 30-8 Self-Induction 30-9 RL Circuits 30-10 Energy Stored in a Magnetic Field 30-11 Energy Density of a Magnetic Field 30-12 Mutual Induction 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-1 What Is Physics? we discussed the fact that a current produces a magnetic field. That fact came as a surprise to the scientists who discovered the effect. A magnetic field can produce an electric field that can drive a current. This link between a magnetic field and the electric field it produces (induces) is now called Faraday’s law of induction. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-2 Two Experiments A current appears only if there is relative motion between the magnet and the loop. The current generated is known as “induced current”; the emf that appears is known as “induced emf”; the whole effect is called “induction”. Loop 1 Loop 2 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-3 Faraday’s Law of Induction Magnetic Flux ФB SI magnetic flux unit: T‧m² known as the Weber (symbol Wb). 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-1 The long solenoid S shown (in cross section) in Figure has 220 turns/cm and carries a current i = 1.5 A; its diameter D is 3.2 cm. At its center we place a 130-turn closely packed coil C of diameter d = 2.1 cm. The current in the solenoid is reduced to zero at a steady rate in 25 ms. What is the magnitude of the emf that is induced in coil C while the current in the solenoid is changing? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-1 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-1 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-4 Lenz’s Law An induced current has a direct such that the magnetic field due to the induced opposes the change in the magnetic flux that induces the current. Opposition to pole movement 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-4 Lenz’s Law Opposition to flux change 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-2 Figure shows a conducting loop consisting of a half-circle of radius r = 0.20 m and three straight \ sections. The half-circle lies in a uniform magnetic field that is directed out of the B page; the field magnitude is given by B= 4.0t2+2.0t +3.0, with B in teslas and t in seconds. An ideal battery with emf εbat = 2.0V is connected to the loop. The resistance of the loop is 2.0Ω. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-2 (a) What are the magnitude and direction of the emfεind induced around the loop by field B at t = 10 s? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-2 (b) What is the current in the loop at t =10 s? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-3 Figure shows a rectangular loop of wire immersed in a nonuniform and varying magnetic field that is perpendicular B to and directed into the page. The field’s magnitude is given by B= 4t2x2, with B in teslas, t in seconds, and x in meters. The loop has width W =3.0 m and height H= 2.0 m. What are the magnitude and direction of the induced emf ε around the loop at t= 0.10 s? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-3 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-5 Induction and Energy Transfers 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-5 Induction and Energy Transfers 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-5 Induction and Energy Transfers Eddy currents 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-6 Induced Electric Fields A change magnetic field produces an electric field 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-4 In Figure, take R =8.5 cm and dB/dt = 0.13 T/s. (a) Find an expression for the magnitude E of the induced electric field at points within the magnetic field, at radius r from the center of the magnetic field. Evaluate the expression for r = 5.2 cm. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-4 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-4 In Figure, take R =8.5 cm and dB/dt = 0.13 T/s. (b) Find an expression for the magnitude E of the induced electric field at points that are outside the magnetic field, at radius r. Evaluate the expression for r = 12.5 cm. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-4 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-7 Inductors and Inductance 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-7 Inductors and Inductance SI unit for L : the Henry (symbol: H) An inductor has inductance L=1H, if a current change of 1A/s results in a self-induced emf of 1V. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-8 Self-Induction loop 1 loop 2 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-9 RL Circuits 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-5 Figure shows a circuit that contains three identical resistors with resistance R = 9.0 Ω, two identical inductors with inductance L = 2.0 mH, and an ideal battery with emfε=18 V. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-5 (a) What is the current i through the battery just after the switch is closed? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-5 (b) What is the current i through the battery long after the switch has been closed? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-6 A solenoid has an inductance of 53 mH and a resistance of 0.37Ω. If the solenoid is connected to a battery, how long will the current take to reach half its final equilibrium value? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-10 Energy Stored in a Magnetic Field 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-10 Energy Stored in a Magnetic Field 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-7 A coil has an inductance of 53 mH and a resistance of 0.35Ω.If a 12 V emf is applied across the coil, how much energy is stored in the magnetic field after the current has built up to its equilibrium value? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-7 A coil has an inductance of 53 mH and a resistance of 0.35Ω.After how many time constants will half this equilibrium energy be stored in the magnetic field? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-7 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

30-11 Energy Density of a Magnetic Field 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-8 A long coaxial cable consists of two thin-walled concentric conducting cylinders with radii a and b. The inner cylinder carries a steady current i, and the outer cylinder provides the return path for that current. The current sets up a magnetic field between the two cylinders. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-8 (a) Calculate the energy stored in the magnetic field for a length l of the cable. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-8 (b) What is the stored energy per unit length of the cable if a = 1.2 mm, b = 3.5 mm, and i =2.7 A? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-12 Mutual Induction 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 30-12 Mutual Induction The SI unit for M: the Henry (H) 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-9 Figure shows two circular close-packed coils, the smaller (radius R2, with N2turns) being coaxial with the larger (radius R1, with N1turns) and in the same plane. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-9 (a) Derive an expression for the mutual inductance M for this arrangement of these two coils, assuming that R1>> R2. 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 Example 30-9 (b) What is the value of M for N1= N2 = 1200 turns, R2= 1.1 cm, and R1= 15 cm? 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授

普通物理教材-30，國立彰化師範大學物理系/郭艷光教授 End of chapter 30! 2018/12/7 普通物理教材-30，國立彰化師範大學物理系/郭艷光教授