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chapter32

# chapter32 - Chapter 32 Inductance Joseph Henry 1797 1878...

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Chapter 32 Inductance

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Joseph Henry z 1797 – 1878 z American physicist z First director of the Smithsonian z Improved design of electromagnet z Constructed one of the first motors z Discovered self-inductance z Unit of inductance is named in his honor
Some Terminology z Use emf and current when they are caused by batteries or other sources z Use induced emf and induced current when they are caused by changing magnetic fields z When dealing with problems in electromagnetism, it is important to distinguish between the two situations

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Self-Inductance z When the switch is closed, the current does not immediately reach its maximum value z Faraday’s law can be used to describe the effect
Self-Inductance, 2 z As the current increases with time, the magnetic flux through the circuit loop due to this current also increases with time z This increasing flux creates an induced emf in the circuit

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Self-Inductance, 3 z The direction of the induced emf is such that it would cause an induced current in the loop which would establish a magnetic field opposing the change in the original magnetic field z The direction of the induced emf is opposite the direction of the emf of the battery z This results in a gradual increase in the current to its final equilibrium value
Self-Inductance, 4 z This effect is called self-inductance z Because the changing flux through the circuit and the resultant induced emf arise from the circuit itself z The emf ε L is called a self-induced emf

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Self-Inductance, Equations z An induced emf is always proportional to the time rate of change of the current z The emf is proportional to the flux, which is proportional to the field and the field is proportional to the current z L is a constant of proportionality called the inductance of the coil and it depends on the geometry of the coil and other physical characteristics L dI ε L dt =−
Inductance of a Coil z A closely spaced coil of N turns carrying current I has an inductance of z The inductance is a measure of the opposition to a change in current BL N ε L Id I d t Φ ==

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Inductance Units z The SI unit of inductance is the henry (H) z Named for Joseph Henry A s V 1 H 1 =
Inductance of a Solenoid z Assume a uniformly wound solenoid having N turns and length z Assume is much greater than the radius of the solenoid z The flux through each turn of area A is Bo o N BA μ nIA μ IA Φ= = = l

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Inductance of a Solenoid, cont z The inductance is z This shows that L depends on the geometry of the object 2 o B μ NA N L I Φ == l
RL Circuit, Introduction z A circuit element that has a large self- inductance is called an inductor z The circuit symbol is z We assume the self-inductance of the rest of the circuit is negligible compared to the inductor z However, even without a coil, a circuit will have some self-inductance

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Effect of an Inductor in a Circuit z The inductance results in a back emf z Therefore, the inductor in a circuit opposes changes in current in that circuit z
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chapter32 - Chapter 32 Inductance Joseph Henry 1797 1878...

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