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Unformatted text preview: Inductance Chapter 30 Take a length of copper wire and wrap it around an oatmeal box to form a coil. Place the coil in an electric circuit, does it behave any differently than the same wire when straight? The answer is yes. Your car has a coil mounted near the engine that can turn your 12 volt battery into 20,000 volts. Coils also keep florescent lights shinning. A changing current in a coil induces an emf in an adjacent coil . The coupling between the coils is described by their mutual inductance . Lowvalue inductors. Symbol for an inductor Inductors A changing current in a coil induces an emf in the same coil . Such a coil is called an inductor and the relationship of current to emf is described by its inductance (also self inductance). If a coil is initially carrying a current, energy is released when the current decreases ; this principle is used in automotive ignition systems. Mutual Self Inductance Consider the magnetic interaction of two wires carrying steady currents. The current in one wire causes a magnetic field, which exerts a force on the current in the second wire. But and additional interaction arises between two circuits when there is a changing current in one of the circuits . Consider two neighboring coils of wire. A current flowing in say the coil to the left, produces a Bfield and hence a magnetic flux through the coil on the right. If the current in the left coil changes the flux in the coil in the right changes (since B = nI) (the flux of the instantaneous B field is BA), then t his changing magnetic flux according to Faradays law of induction produces and emf in the coil on the right . In this way the current in one coil can and does induce a current in the second coil . As shown, a current i 1 in coil 1 sets up a magnetic field. Some of these magnetic field lines pass through coil 2 and hence there exists a magnetic flux B2 through coil 2 . The magnetic flux B2 is therefore proportional to the current i 1 of coil 1 . If i 1 changes, then B2 changes correspondingly and induces an emf in coil 2 given by: dt d N B 2 2 2  = By introducing a proportionality constant M 21 , called the mutual inductance of two coils, and from the preceding information, we have: Hence by taking the time derivative on each side we have: dt di M dt d N B 1 21 2 2 = 1 21 2 2 i M N B = Hence: dt di M 1 21 2 = That is a change in current i 1 in coil 1 induces an emf in coil 2 that is directly proportional to the rate of change of i 1 . 1 21 2 2 i M N B = From the above equation the mutual inductance is defined to be: 1 2 2 21 i N M B If the coils are in a vacuum, the flux B2 through coil 2 is directly proportional to i 1 ....
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 Summer '09
 W.CHRISTENSEN
 Physics, Inductance

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