Lecture 13.2 :! Inductors

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1 Lecture 13.2 :! Inductors Lecture Outline:! Induced Fields! Inductors! LC Circuits! LR Circuits!! Textbook Reading:! Ch April 9,

2 Announcements! HW #10 due on Tuesday, April 14, at 9am.! Exam #3 next Thursday, April 16. Will cover Ch. 32 and Ch. 33. Bring your calculators and one sheet of notes.!! 2

3 Last Lecture... All induced currents are associated with a changing magnetic flux. Two ways flux can change:! 1.Geometry: Loop can expand, contract, or rotate.! 2.Magnetic field can change. E = d m dt = B da dt + A db dt 3

4 Last Lecture... We know from Lenz s law that a conducting loop in a changing magnetic field will develop an induced current to counteract the changing flux. There must be an E-field present to create this current in the loop. In this changing magnetic field, the E-field is present whether or not the loop is there! 4

5 Clicker Question #1 The induced emf around this loop is! A. 200 V. B. 50 V. C. 2 V. D. 0.5 V. E V. 5

6 Clicker Question #1 The induced emf around this loop is! A. 200 V. B. 50 V. C. 2 V. D. 0.5 V. E V. 5

7 Clicker Question #1 The induced emf around this loop is! A. 200 V. B. 50 V. C. 2 V. D. 0.5 V. E V. Is the induced current flowing clockwise or counterclockwise? 5

8 The Can Crusher Demo 6

9 The Can Crusher Demo 6

10 Induced Fields We now understand that a changing magnetic field creates an electric field (even though no charge is present). We can rewrite Faraday s law to allow calculation of the electric field. (Work done moving a charge around a closedloop in an electric field E) W closed curve = q E ds 7

11 Induced Fields We now understand that a changing magnetic field creates an electric field (even though no charge is present). We can rewrite Faraday s law to allow calculation of the electric field. (Work done moving a charge around a closedloop in an electric field E) W closed curve = q E ds Potential difference (EMF) crossed around that closed-loop path. E = W closed curve q = E ds 7

12 Induced Fields We now understand that a changing magnetic field creates an electric field (even though no charge is present). We can rewrite Faraday s law to allow calculation of the electric field. (Work done moving a charge around a closedloop in an electric field E) W closed curve = q E ds Potential difference (EMF) crossed around that closed-loop path. E = W closed curve q = E ds (for the case of an unchanging loop perpendicular to B-field) E ds = A db dt 7

13 Induced Fields Inside a solenoid, a changing magnetic field induced an electric field that circles around the magnetic field. 8

14 Induced Fields Inside a solenoid, a changing magnetic field induced an electric field that circles around the magnetic field. 8

15 Induced Fields Inside a solenoid, a changing magnetic field induced an electric field that circles around the magnetic field. 8

16 Induced Fields Maxwell knew of Faraday s work, and based on symmetry he proposed that a changing electric field induces a magnetic field. 9

17 Induced Fields Maxwell (~1855) also predicted that electromagnetic waves with transverse E and B fields would travel at the speed of light. v em wave = 1 0µ m/s 10

18 Induced Fields Maxwell (~1855) also predicted that electromagnetic waves with transverse E and B fields would travel at the speed of light. v em wave = 1 0µ m/s 10

19 Inductors Inductors are devices in circuits that can be used to store energy in magnetic fields (similar to Capacitors storing energy in electric fields). They have interesting behavior when placed in circuits. Inductance L I m 1 henry = 1 H 1Wb/A = 1 Tm 2 /A 11

20 Inductors What s the inductance of an N turn solenoid? Recall (from Ampere s Law): B solenoid = µ 0NI l 12

21 Inductors If (and only if) the current through an inductor is changing, a potential difference develops across the inductor. Induced current Induced field 13

22 Inductors If (and only if) the current through an inductor is changing, a potential difference develops across the inductor. Induced current Induced field 13

23 Inductors If (and only if) the current through an inductor is changing, a potential difference develops across the inductor. Induced current Induced field V L = d m dt = L di dt We choose same sign convention as in resistors...voltage decreases in direction of current flow. 13

24 Clicker Question #2 Which current is changing more rapidly?! A. Current I 1. B. Current I 2. C. They are changing at the same rate. D. Not enough information to tell. 14

25 Clicker Question #2 Which current is changing more rapidly?! A. Current I 1. B. Current I 2. C. They are changing at the same rate. D. Not enough information to tell. 14

26 Inductors 15

27 Inductors How much energy is stored in the magnetic field of an inductor? 16

28 LC Circuits A circuit with an inductor and capacitor arranged in series is called a LC circuit. The current in this circuit will oscillate in time. 17

29 LC Circuits 18

30 LR Circuits A circuit with an inductor and resistor arranged in series is called a LR circuit. 19

31 Reminders! HW #10 due on Tuesday.! Exam #3 next Thursday. 20

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