chapter29

# chapter29 - 2 noitcaretni citengamortcele elgnis a fo...

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Electromagnetic induction r r kQ E ˆ 2 = v 2 0 ˆ 4 r r v q B × = v v π µ So far we have found that Electric charges create E-fields Moving electric charges create B-fields But this is not the whole story! 2 Electromagnetic induction Electric Fields can also be created by a changing Magnetic Field. Magnetic Fields can also be created by a changing Electric Field. This is described by “Faraday’s Law”. This will help complete the set of equations called Maxwell’s equations of electricity and magnetism. Electricity and Magnetism can be unified in a single theory! The electricity and magnetic forces are manifestations of a single “electromagnetic interaction”

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Electromagnetic induction Magnetic Flux
Magnetic Flux The flux through an element of area is: To calculate the flux through the surface, we need to integrate: For the simple case of a flat surface, we obtain: B φ Magnetic flux

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7 Clicker Question At what angle of orientation of the surface is the flux through the surface half of the maximum possible flux? A) φ = 0 degrees B) φ = 30 degrees C) φ = 45 degrees D) φ = 60 degrees E) None of the above B φ Faraday’s Law of Induction 8 dt d B Φ = ε Two new quantities introduced. 1. Magnetic Flux = Φ B 2. Electro Motive Force (EMF) = ε A changing (time-dependent) magnetic field “induces” (generates) an EMF ε . The magnitude of the EMF equals minus the rate of change of the flux.
Important observations: Recall: EMF is not a force, but a source of voltage capable of generating power. The EMF is called “motional” EMF, to distinguish from “chemical” EMF (batteries) Recall: The magnetic flux through a closed surface is zero! (Gauss’ Law for B-fields) The surface for Faraday’s Law is an open surface! 10 Clicker Question We have a square imaginary loop with side of length a. There is a Magnetic Field that is uniform throughout the region as shown. How does the Magnetic Flux magnitude | Φ B | change if we halve the Magnetic Field strength and double the sides of the square loop? A) Flux goes to ½ original value B) Flux goes to ¼ original value C) Flux goes to 2 times original value D) Flux does not change E) None of the above X B

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Changing the magnetic flux 11 1. Change the strength of the Magnetic Field 2. Change the area of the loop 3. Change the orientation of the loop (A vector) and the B-field 12 A loop of wire is moving rapidly through a uniform magnetic field as shown. Is a non-zero EMF induced in the loop? A) No, there in no EMF B) Yes, there is an EMF Clicker Question
A loop of wire is spinning rapidly about a stationary axis in uniform magnetic field as shown. True or False: There is a non-zero EMF induced in the loop. A) False, zero EMF

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