field is proportional to current I Thus L is a constant of proportionality Self

Field is proportional to current i thus l is a

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field is proportional to current IThus L is a constant of proportionalitySelf-inductance is a measure of opposition to a changein currentIΦNLsoLIΦN
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Self-Inductance: SolenoidUniformly wound solenoid has Nturns and length is much greater than radius of solenoidNumber of turns per unit length is n = N/ℓMagnetic field B in center of solenoid isIIooNBμ nμ
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Self-Inductance: SolenoidMagnetic flux through each turn isTherefore, self-inductance LisSelf-inductance of solenoid isLdepends only on geometry of objectIBoNABAμ2IBoNμ N ALAnμL20
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Energy Stored in an InductorGenerator moves a small charge ΔQ = IΔt through a potential difference E = - L ΔI / Δt Work done is ΔW = -(I Δt)(-L ΔI / Δt) = L I ΔI Adding all ΔWgives W = ½ L I 2Energy Stored in inductor isEnergy = U = ½ L I 2
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Energy Density in Magnetic FieldEnergy stored in a solenoidisEnergy densityin magnetic field is energy per unit volume (ℓA)General expression valid for allmagnetic fieldsABμ21UA)nIμ(μ21I)Anμ(21U2020022020BBμ21VolumeU
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9. TransformersTransformer changes voltage of AC current Uses magnetic inductionPrimary coil is connected to a generatorSecondary coil has an emf induced in it
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TransformerAC transformer:two coils of wire wound around a core of soft ironPrimaryis input side connected to AC generatorhas N1turns
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TransformersSecondary is output side connected to a resistor or “load”has N2turnsIron used as core material has a high permeability μincreases magnetic flux provides a path for flux to pass through coilsEddy current losses are minimized by using laminated iron core
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Transformer EquationsPrimarySecondaryTransformer equationPower in primary equals power in secondary Power factor cosφ = 1tΔΔΦNppEtΔΔΦNssEpspsNNEEspsppsNNVVIIssppIIPEEssppVandVEE
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Transformers and Power TransmissionVoltage from power plant is stepped upPower transmitted at high voltage, small lossVoltage stepped down to use in home
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10. Concept SummaryInduced emf and induced currentMotional emfMagnetic fluxFaraday’s law and Lenz’s lawElectric generatorMutual inductance and self-inductanceMagnetic energy stored in inductorMagnetic energy densityTransformers
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  • Spring '20
  • Magnetic Field, Heinrich Lenz

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