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Chapter 29 Continued-Chapter 31- Chapter 32

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29-3 EMF Induced in a Moving Conductor Example 29-8: Force on the rod. To make the rod move to the right at speed v, you need to apply an external force on the rod to the right. (a) Explain and determine the magnitude of the required force. (b) What external power is needed to move the rod?

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Electric Generators Same Principle as a motor: Motor: loop turns due to current in B Generator: current flows due to turning loop in B http://www.youtube.com/watch?v=zOdboRY f1hM http://www.youtube.com/watch?v=TU8G KV2TXxo

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A generator is the opposite of a motor – it transforms mechanical energy into electrical energy. This is an ac generator: The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings. 29-4 Electric Generators

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If the loop is rotating with constant angular velocity ω, the induced emf is sinusoidal: For a coil of N loops,

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29-4 Electric Generators Example 29-9: An ac generator. The armature of a 60-Hz ac generator rotates in a 0.15-T magnetic field. If the area of the coil is 2.0 x 10 -2 m 2, how many loops must the coil contain if the peak output is to be E 0 = 170 V?

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A transformer is a device for increasing or decreasing an ac voltage A transformer consists of two coils, either interwoven or linked by an iron core. A changing emf in one induces an emf in the other. The ratio of the emfs is equal to the ratio of the number of turns in each coil: 29-6 Transformers and Transmission of Power

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This is a step-up transformer – the emf in the secondary coil is larger than the emf in the primary and N s > N p 29-6 Transformers and Transmission of Power

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Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio of turns: 29-6 Transformers and Transmission of Power

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Example 29-12: Cell phone charger. The charger for a cell phone contains a transformer that reduces 120-V ac to 5.0- V ac to charge the 3.7-V battery. (It also contains diodes to change the 5.0-V ac to 5.0-V dc.) Suppose the secondary coil contains 30 turns and the charger supplies 700 mA. Calculate (a) the number of turns in the primary coil, (b) the current in the primary, and (c) the power transformed.

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Transformers work only if the current is changing; this is one reason why electricity is transmitted as ac. 29-6 Transformers and Transmission of Power

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A changing magnetic flux induces an electric field; this is a generalization of Faraday’s law. The electric field will exist regardless of whether there are any conductors around: 29-7 A Changing Magnetic Flux Produces an Electric Field.

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31-3 Maxwell’s Equations This set of equations describe electric and magnetic fields, and is called Maxwell’s equations. In the absence of dielectric or magnetic materials, they are:

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Since a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field, once sinusoidal fields are created they can propagate on their own. These propagating fields are called electromagnetic waves (EM). 31-4 Production of Electromagnetic Waves

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Induced Electric Fields Electric & Magnetic fields induce each other http://www.walter-fendt.de/ph14e/emwave.htm Changing E changing B Changing B induces emf changing E create electromagnetic waves

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Electromagnetic Waves Waves made of oscillating electric and magnetic fields Produced by ACCELERATING charges E B

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Electromagnetic Waves Charge accelerates this creates a changing B-field By Faraday’s Law of induction this creates a changing E-field E B

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31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations B and E are related by the following equation Here, v is the velocity of the wave..

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31-5 Electromagnetic Waves, and Their Speed, Derived from Maxwell’s Equations The magnitude of this speed is around 3.0 x 10 8 m/s – precisely equal to the measured speed of light.

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Speed of EM Waves -- vacuum EM waves do not require a medium to propagate Permittivity of free space = 8.85 x 10 -12 C 2 /N m 2 Permeability of free space: = 4 x 10 -7 T m/A Galaxy 2 million ly away

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The frequency of an electromagnetic wave is related to its wavelength and to the speed of light: 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

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Speed of Light in matter Generally light slows down when it encounters a medium other than vacuum. n is the index of refraction of the medium n≥1 c n v Frequency is unchanged

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Electromagnetic waves can have any wavelength; we have given different names to different parts of the wavelength spectrum. 31-6 Light as an Electromagnetic Wave and the Electromagnetic Spectrum

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Chapter 32 Light: Reflection and Refraction

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Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics. 32-1 The Ray Model of Light

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Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence. 32-2 Reflection; Image Formation by a Plane Mirror

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