物理与光电工程学院：《大学物理》课程PPT教学课件（讲稿，英文第三版）Chapter 28 Inductance and Electromagnetic Oscillations

Chapter 28 Inductance and Electromagnetic Oscillations Chapter 28 Inductance and Electromagnetic Oscillations 1. Self and Mutual Induction 2. Energy Stored in a Magnetic Field

Chapter 28 Inductance and Electromagnetic Oscillations Chapter 28 Inductance and Electromagnetic Oscillations 1. Self and Mutual Induction 2. Energy Stored in a Magnetic Field

Chapter 28 Inductance and Electromagnetic Oscillations New words and expressions self induction 自感应 inductance 感应系数 mutual induction 互感应 Inductor 感应器,电感线圈

Chapter 28 Inductance and Electromagnetic Oscillations New words and expressions self induction 自感应 inductance 感应系数 mutual induction 互感应 Inductor 感应器, 电感线圈

Chapter 28 Inductance and Electromagnetic Oscillations 28-2 Self-Induction 1. SelfInduction(自感应)(P645-647 The process that an induced emf appear in any coil in which the current is changing is called self-induction(由于自己线路中的电流的变化而在自 己的线路中产生感应电流的现象一一自感现象) If we establish a current l in the coil, the magnetic flux linkage Na is proportional to 1, ∝ Define proportionality constant is L, y=LI

Chapter 28 Inductance and Electromagnetic Oscillations 28-2. Self-Induction The process that an induced emf appear in any coil in which the current is changing is called self-induction (由于自己线路中的电流的变化而在自 己的线路中产生感应电流的现象－－自感现象). 1. Self-Induction (自感应)(P645-647): If we establish a current I in the coil, the magnetic flux linkage N is proportional to I,   I Define proportionality constant is L,  = LI

Chapter 28 Inductance and Electromagnetic Oscillations Then the coefficient is defined as the self-Inductance NΦ L= A coil that has significant self- inductance l is called an inductor Its si unit: henry(亨利)=1H=1Tm2/A related to the geometry of the coils and magnetic medium.自感系数与线圈的大小、形状、 磁介质、线圈密度有关,而与线圈中电流无关

Chapter 28 Inductance and Electromagnetic Oscillations I N L  = Then the coefficient L is defined as the Self-Inductance. A coil that has significant self￾inductance L is called an inductor. It related to the geometry of the coils and magnetic medium. 自感系数与线圈的大小、形状、 磁介质、线圈密度有关，而与线圈中电流无关。 1 henry (亨利) = 1 H = 1T.m2 Its SI unit: /A

Chapter 28 Inductance and Electromagnetic Oscillations 2. Self-Induction EMe The emf appears in self-induction is called self- induced emf It obeys Faraday's law ofinduction d d(NΦ) dt dt Y=LI dⅠ fl is constant E;=-L dt The minus sign indicates that the self-induced emf has the orientation such that it opposes the change in 1

Chapter 28 Inductance and Electromagnetic Oscillations The emf appears in self-induction is called self￾induced emf. It obeys Faraday’s law of induction. The minus sign indicates that the self-induced emf has the orientation such that it opposes the change in I. 2. Self-Induction EMF t i N d d  = − where  = LI If L is constant t I i L d d  = − t N d d( ) = − dt d = −

Chapter 28 Inductance and Electromagnetic Oscillations 3. Calculation of self-Induction ①假设线圈中的电流Ⅰ; ②求线圈中的磁通量Φ; ③由定义求出自感系数L L

Chapter 28 Inductance and Electromagnetic Oscillations 3. Calculation of Self-Induction ①假设线圈中的电流 I ； ②求线圈中的磁通量 ； ③由定义求出自感系数 L。 I L  = 

Chapter 28 Inductance and Electromagnetic Oscillations Example: Inductance of a Solenoid 长直螺线管,线圈密度为n,长度为l,横截面积为 S,插有磁导率为的磁介质,求线圈的自感系数L。 Solution:先设电流Ⅰ—根据安培环路定理求得H→B →L Magnetic field inside the solenoid of length l is: Bs√ Ponl

Chapter 28 Inductance and Electromagnetic Oscillations Example: Inductance of a Solenoid. nI l NI B 0 0   = = Magnetic field inside the solenoid of length l is: 一长直螺线管，线圈密度为 n，长度为 l，横截面积为 S，插有磁导率为  的磁介质，求线圈的自感系数 L 。 l S  E Solution: 先设电流 I 根据安培环路定理求得 H B Φ L

Chapter 28 Inductance and Electromagnetic Oscillations Magnetic flux linkage: NR=nlBA=(monIn)op2/s L=N①B_∠ImR2n2l =/0n2S The inductance per unit length for a long solenoid near its center 2=10nS Inductance l like capacitance--depends only on the geometry of the device

Chapter 28 Inductance and Electromagnetic Oscillations 2 2 0 NB = nlBA = ( n lI)R Magnetic flux linkage: n lS I I R n l I L B 2 0 2 2 N 0    = =  = l S  E The inductance per unit length for a long solenoid near its center, n S l L 2 = 0 Inductance L —— like capacitance ——depends only on the geometry of the device

Chapter 28 Inductance and Electromagnetic Oscillations Example: calculating self-inductance of co-axis wire 有两个同轴圆筒形导体,其半径 R 分别为R和R,通过它们的电流 均为Ⅰ,但电流的流向相反设在 两圆筒间充满磁导率为/的均匀 磁介质,求其自感L Solution: B czar r

Chapter 28 Inductance and Electromagnetic Oscillations Example: Calculating self-inductance of co-axis wire. r I B   2 0 = 1 R2 R  r  Solution: 有两个同轴圆筒形导体 , 其半径 分别为 和 , 通过它们的电流 均为 , 但电流的流向相反.设在 两圆筒间充满磁导率为 的均匀 磁介质 , 求其自感L. R1 R2 I  L R1 I R2 l I r

Chapter 28 Inductance and Electromagnetic Oscillations 如图在两圆筒间取一长 为l的面PQRS,并将其分 R 成许多小面元 d④=B·dS=Bldn ①=d￠= R2 ldr ri Zt r R R 2 2T R

Chapter 28 Inductance and Electromagnetic Oscillations 如图在两圆筒间取一长 为 的面 , 并将其分 成许多小面元. l PQRS Φ B S   d = d = Bldr l r r I Φ Φ R R d 2π d 2 1   = =  1 2 ln 2π R Il R Φ  = R1 I S P R Q R2 l I r dr