Tuesday, 9 August 2016
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1 Tuesday, 9 August 2016
2 Conceptual Problem a When the switch on the left is closed, which direction does current flow in the meter on the right: 1. Right to left 2. Left to right 3. There is no induced current
3 Conceptual Problem a When the switch on the left is closed, which direction does current flow in the meter on the right: 1. Right to left 2. Left to right 3. There is no induced current
4 QuickCheck The induced emf around this loop is A. B. C. D. E. 200 V. 50 V. 2 V. 0.5 V V. Slide 33-78
5 QuickCheck The induced emf around this loop is A. B. C. D. E. 200 V. 50 V. 2 V. 0.5 V V.
6 Ability to calculate! Recipe: 1) Direction: 2) Flux 3) Faraday's Law Bind I ind B da d EMF dt
7 Example 2: Changing B The magnetic field can be described as 2 2 B=(5 mt / s ) t (3 mt / s) t into the page. What is the direction and magnitude of the current in the loop at t=0s? The resistance in the loop is 0.25Ω. The area of the loop is 10.cm2.
8 Example: how does a microphone work? 1) Describe how the magnetic flux through the coil is changing as the magnet moves as shown? 2) What is the average EMF (voltage) produced in the coil as the magnet moves from 10 cm to 3 cm away from the coil? 3) Which way is the induced current in the coil flowing where the coil crosses the positive x axis?
9
10 The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing? A. Yes. B. No.
11 The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing? A. Yes. B. No.
12 QuickCheck 33.6 The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing? A. Yes. B. No. Slide 33-52
13 QuickCheck 33.6 The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing? A. Yes. B. No. Slide 33-53
14 Example 3: Changing θ
15 Homework 7 Problem2
16 Now you are ready to consider other examples where
17 Magnetic Flux in a Nonuniform Field The figure shows a loop in a nonuniform magnetic field. The total magnetic flux through the loop is found with an area integral. Slide 33-54
18 Application Transformer A transformer sends an alternating emf V1 through the primary coil. This causes an oscillating magnetic flux through the secondary coil and, hence, an induced emf V2. The induced emf of the secondary coil is delivered to the load: Slide 33-98
19 Transformers A step-up transformer, with N2 >> N1, can boost the voltage of a generator up to several hundred thousand volts. Delivering power with smaller currents at higher voltages reduces losses due to the resistance of the wires. High-voltage transmission lines carry electric power to urban areas, where stepdown transformers (N2 << N1) lower the voltage to 120 V. Slide 33-99
20 The primary coil of a transformer is connected to a battery, a resistor, and a switch. The secondary coil is connected to an ammeter. When the switch is thrown closed, the ammeter shows 1. zero current. 2. a nonzero current for a short instant. 3. a steady current.
21 The primary coil of a transformer is connected to a battery, a resistor, and a switch. The secondary coil is connected to an ammeter. When the switch is thrown closed, the ammeter shows 1. zero current. 2. a nonzero current for a short instant. 3. a steady current.
22 The potential difference across R is 1. VN2 /N1. 2. VN1/N2. 3. V. 4. zero. 5. insufficient information
23 The potential difference across R is 1. VN2 /N1. 2. VN1/N2. 3. V. 4. zero. 5. insufficient information
24 Induced EMF => induced electric field The figure shows a conducting loop in an increasing magnetic field. Slide 33-80
25 The Induced Electric Field Faraday s Law restated Slide 33-81
26 Induced Electric Field in a Solenoid Slide 1 of 3 What electric field is induced by the current?
27 Induced Electric Field in a Solenoid Slide 1 of 3 What electric field is induced by the current? Slide 33-82
28 Induced Electric Field in a Solenoid Slide 1 of 3 What electric field is induced by the current?
29 Induced Electric Field in a Solenoid Slide 1 of 3 What is the electric field induced by the current inside the solenoid?
30 Induced Electric Field in a Solenoid Slide 3 of 3 To use Faraday s law, integrate around a clockwise circle of radius r: Thus the strength of the induced electric field inside the solenoid is: Slide 33-84
31 QuickCheck The magnetic field is decreasing. Which is the induced electric field? E. There s no induced field in this case. Slide 33-89
32 QuickCheck The magnetic field is decreasing. Which is the induced electric field? The field is the same direction as induced current would flow if there were a loop in the field. E. There s no induced field in this case. Slide 33-90
33 The Induced Electric Field Slide 33-91
34 The Induced Magnetic Field As we know, changing the magnetic field induces a circular electric field. Symmetrically, changing the electric field induces a circular magnetic field. The induced magnetic field was first suggested as a possibility by James Clerk Maxwell in Slide 33-92
35 Maxwell s Theory of Electromagnetic Waves A changing electric field creates a magnetic field, which then changes in just the right way to recreate the electric field, which then changes in just the right way to again recreate the magnetic field, and so on. This is an electromagnetic wave. Slide 33-93
36 Inductors
37 Faraday Changing magnetic field produces an electric field around the ring! NOT A POTENTIAL like a battery! B ΔB d EMF dt IR EMF
38 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.
39 Faraday and Inductance Changing current produces electro-motive force: Self-Induction B di V L dt
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