ch30_lecture_notes

# ch30_lecture_notes - Chapter 30 Faraday's law Using...

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Chapter 30 Faraday’s law Using Ampere’s law in chapter 29 we investigated how an electric current I can generate a magnetic field B . In this chapter we shall study the fourth (and last) of Maxwell’s equations known as Faraday’s law . Faraday’s law tells us how a magnetic flux Φ B that changes with time can generate an electric field E All electric power generation is based on Faraday’s law.

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A I A I + - In 1831 Faraday discovered that if the magnetic flux Φ B through a closed circuit changes with time as shown in fig.a, then a voltage E appears, as if there were a battery in the circuit, as shown in fig.b. This emf is called an “ induced emf . The resulting current can be measured by the ammeter in the circuit and is known as “ induced ” current. The whole phenomenon is called “ magnetic induction Fig.b Fig.a Φ B (t) E
A B n θ Faraday’s law The induced emf in a circuit is equal to rate of change (with a negative sign) of the magnetic flux through the circuit. Magnetic flux Φ B = BAcos θ (for uniform B ) The magnetic flux Φ B depends on B, A, and θ We can have a time-varying magnetic flux if: • B changes with t θ changes with t • A changes with t B d dt Φ =− E

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In fig.(a) we change B with time as we approach the bar magnet closer to the wire loop. In fig.(d) we we change the angle θ between B (generated by the upper loop) and the normal n to the lower loop. The magnetic flux through the lower loop varies with t B θ n B

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Example 30-2 (page 851) B o = 1 T L = 0.1 m R = 0.065 v = 0.1 m/s I = ? n L 1 vt () 11 cos0 0.15 R oo Bo o B o BA A LL L L v t AL L v t B L L v t BLv d I A dt R Φ= = = = − → =− Φ = Φ = = = = E E
A B n θ Faraday’s Law The minus sign in Faraday’s law indicates the direction in which the current I will flow in the loop of the figure above.

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ch30_lecture_notes - Chapter 30 Faraday's law Using...

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