field is proportional to current IThus L is a constant of proportionalitySelf-inductance is a measure of opposition to a changein currentIΦNLsoLIΦN
Self-Inductance: SolenoidUniformly wound solenoid has Nturns and length ℓℓis much greater than radius of solenoidNumber of turns per unit length is n = N/ℓMagnetic field B in center of solenoid isIIooNBμ nμ
Self-Inductance: SolenoidMagnetic flux through each turn isTherefore, self-inductance LisSelf-inductance of solenoid isLdepends only on geometry of objectIBoNABAμ2IBoNμ N ALAnμL20
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
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
9. TransformersTransformer changes voltage of AC current Uses magnetic inductionPrimary coil is connected to a generatorSecondary coil has an emf induced in it
TransformerAC transformer:two coils of wire wound around a core of soft ironPrimaryis input side connected to AC generatorhas N1turns
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
Transformer EquationsPrimarySecondaryTransformer equationPower in primary equals power in secondary Power factor cosφ = 1tΔΔΦNppEtΔΔΦNssEpspsNNEEspsppsNNVVIIssppIIPEEssppVandVEE
Transformers and Power TransmissionVoltage from power plant is stepped upPower transmitted at high voltage, small lossVoltage stepped down to use in home
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