The SI unit of inductance is the henry, defined as:

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1 Inductors A coil of wire, or solenoid, can be used in a circuit to store energy in the magnetic field. We define the inductance of a solenoid having N turns, length l and cross-section area A as: The SI unit of inductance is the henry, defined as: 1 henry = 1 H = 1 Wb/A = 1 T m2/a A coil of wire used in a circuit for the purpose of inductance is called an inductor. The circuit symbol for an ideal inductor is. Slide

2 Potential Difference Across an Inductor The figure above shows a steady current into the left side of an inductor. The solenoid s magnetic field passes through the coils, establishing a flux. Slide

Therefore the induced magnetic field must point to the right.

3 Potential Difference Across an Inductor In the figure, the current into the solenoid is increasing. This creates an increasing flux to the left. Therefore the induced magnetic field must point to the right. The induced emf V L must be opposite to the current into the solenoid: Slide

4 Potential Difference Across an Inductor In the figure, the current into the solenoid is decreasing. To oppose the decrease in flux, the induced emf V L is in the same direction as the input current. The potential difference across an inductor, measured along the direction of the current, is: Slide

5 Potential Difference Across an Inductor Slide

6 QuickCheck 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. Slide

7 Example 1 - What is the potential difference across a 10 mh inductor if the current through the inductor drops from 150 ma to 50 ma in 10 μs? Does the potential increase or decrease along the direction of the current? Slide

Energy in Inductors and Magnetic Fields As current passes through an inductor, the electric power is: P elec is negative because the current is losing energy.

8 Energy in Inductors and Magnetic Fields As current passes through an inductor, the electric power is: P elec is negative because the current is losing energy. That energy is being transferred to the inductor, which is storing energy U L at the rate: We can find the total energy stored in an inductor by integrating: Slide

9 Energy in Inductors and Magnetic Fields Inside a solenoid, the magnetic field strength is B = μ 0 NI/l. The inductor s energy can be related to B: But Al is the volume inside the solenoid. Dividing by Al, the magnetic field energy density (energy per m 3 ) is: Slide

10 Energy in Electric and Magnetic Fields Slide

11 Example 2 - How much energy is stored in a 3.0-cmdiameter, 12-cm-long solenoid that has 200 turns of wire and carries a current of 0.80 A? Slide

12 LC Circuits The figure shows a capacitor with initial charge Q 0, an inductor, and a switch. The switch has been open for a long time, so there is no current in the circuit. At t 0, the switch is closed. How does the circuit respond? The charge and current oscillate in a way that is analogous to a mass on a spring. Slide

13 LC Circuits: Step A Slide

14 LC Circuits: Step B Slide

15 LC Circuits: Step C Slide

16 LC Circuits: Step D Slide

17 LC Circuits An LC circuit is an electric oscillator. The letters on the graph correspond to the four steps in the previous slides. The charge on the upper plate is Q Q 0 cosωt and the current through the inductor is I I max sinωt, where: Slide

18 QuickCheck If the top circuit has an oscillation frequency of 1000 Hz, the frequency of the bottom circuit is A. 500 Hz. B. 707 Hz. C Hz. D Hz. Slide

LC Circuits A cell phone is actually a very sophisticated two-way radio that communicates with the nearest base station via high-frequency radio waves

19 LC Circuits A cell phone is actually a very sophisticated two-way radio that communicates with the nearest base station via high-frequency radio waves roughly 1000 MHz. As in any radio or communications device, the transmission frequency is established by the oscillating current in an LC circuit. Slide

20 Example 3 - An electric oscillator is made with a 0.10 μf capacitor and a 1.0 mh inductor. The capacitor is initially charged to 5.0 V. What is the maximum current through the inductor as the circuit oscillates? Slide

21 LR Circuits The figure shows an inductor and resistor in series. Initially there is a steady current I 0 being driven through the LR circuit by an external battery. At t 0, the switch is closed. How does the circuit respond? The current through the circuit decays exponentially, with a time constant L/R. Slide

22 LR Circuits Slide

23 QuickCheck What is the battery current immediately after the switch has closed? A. 0 A B. 1 A C. 2 A D. Undefined Slide

24 QuickCheck What is the battery current immediately after the switch has been closed for a very long time? A. 0 A B. 1 A C. 2 A D. Undefined Slide

25 Problem Example 4 - What is the current out of the battery immediately after the switch is closed? What is the current out of the battery after the switch has been closed a long time?

An induced emf is the negative of a changing magnetic field. Similarly, a self-induced emf would be found by

An induced emf is the negative of a changing magnetic field. Similarly, a self-induced emf would be found by This is a study guide for Exam 4. You are expected to understand and be able to answer mathematical questions on the following topics. Chapter 32 Self-Induction and Induction While a battery creates an