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Magnetic Field Basic Concepts: A current carrying wire produces a magnetic field in the area around it. A time changing magnetic field induces a voltage in a coil (wire) if is passes through the coil (transformer) A moving wire in the presence of a magnetic field has a voltage induced in it (generator) A current-carrying wire in the presence of a magnetic field has a force induced on it (motor).

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Faraday’s Law- Induced voltage from a time-varying magnetic field Faraday’s Law for a single wire Faraday’s Law for a coil If we define, : Then we have: Flux linkage

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Ideal Transformer

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Self and Mutual Inductance In a coil In a transformer

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Production of induced force on a wire Direction of l is the same as i

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Vector Product

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Induced voltage on a conductor moving in a magnetic field Direction of l is such that it would make the smallest angle with The positive side of the resulted voltage in where points

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How much do you think the induced voltage is?

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AC excitation of magnetic circuits What do we mean by AC excitation? 1- Inserting sinusoid current (what we have considered so far) 2- Applying sinusoid voltage Q: What happens if we somehow insert sinusoid current to a coil? Will the flux and induced voltage be sinusoid as well? A: No, because of saturation and hysteresis Q: What happens if we apply sinusoid voltage to a coil? Will the flux and current (magnetizing current) be sinusoid as well? A: No, because of saturation and hysteresis Conclusion: In a coil current and voltage cannot be sinusoid simultaneously. If one is sinusoid, the other is not.

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Let’s see what would happen if we apply sinusoid voltage to a coil?

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Magnetization current

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