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Inductors

Inductors. PH 203 Professor Lee Carkner Lecture 20. Finding emf. e = -N(d F /dt) But the magnetic flux depends on the changing current and the properties of the coil e = -L(di/dt) where the constant of proportionality L is the inductance. Inductance.

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Inductors

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  1. Inductors PH 203 Professor Lee Carkner Lecture 20

  2. Finding emf e = -N(dF/dt) • But the magnetic flux depends on the changing current and the properties of the coil e = -L(di/dt) • where the constant of proportionality L is the inductance

  3. Inductance • The unit of inductance is the henry, • Equating the two expressions for e e = L(di/dt) = N(dF/dt) L = N(dF/di) • Inductance is a property of the circuit element • Like resistance or capacitance

  4. Solenoid Inductance • To find L, we need a relationship between F and I for a solenoid • Flux in general: • F = BA cos q or F = BA • B = m0(N/l)i or i = Bl/(m0N) • L = N(dF/di) = NF/i = NBAm0N/Bl = m0N2A/l L = m0n2Al • Note: • N is number of turns, n is number of turns per meter

  5. Inductors • In a circuit any element with a high inductance is represented by an inductor • We will assume that the rest of the circuit has negligible inductance • Symbol is a spiral:

  6. Motional emf • If we make the loop larger or smaller, or move it in or out of a field, we will induce a potential • remember emf is a potential difference (or voltage) • How does motion in a field translate to voltage?

  7. Consider a conductor of length L sliding on a frame with velocity v but Dx = vDt, so DA = LvDt DF/Dt = BDA/Dt = (BLvDt)/Dt e = BLv Motional emf - Derived DA X B field into page v L x Dx in time Dt

  8. Motional emf -- Direction • If the area decreases, the flux decreases and thus the induced B field is in the same direction as the original

  9. Motional emf Energy • How is energy related to motional emf? • The loop feels a magnetic force you have to overcome • The energy goes into the electrical energy of the current in the loop P = i2R

  10. Power and Motional emf • Since e = BLv and e = iR, we can write: i = BLv/R P = B2L2v2/R • Large loops with low resistance moving fast in a large magnetic field will have a lot of electrical energy and thus require more work input

  11. Eddy Currents • Imagine a loop moving out of a magnetic field • If the object is not a loop, circular currents can still be induced which have the same effect • Called eddy currents

  12. Eddy Braking • The field from the eddy currents will produce a force opposite the motion • Can produce magnetic braking • No physical contact with disk, so no wear

  13. Next Time • Read 30.8-30.12 • Problems: Ch 30, P: 21, 29, 31, 48, 51

  14. What is the direction of current in the loop from the PAL (seen from top down)? • clockwise • counterclockwise • left • right • down

  15. A ring undergoes thermal expansion while in a uniform magnetic field. If the current induced in the loop is clockwise, what is the direction of the magnetic field? • left • right • into the page • out of the page • counterclockwise

  16. A bar magnet held north pole up is dropped straight down through a face up coil of wire. What is the direction of the current in the coil as the magnet enters and leaves the coil? • clockwise, counterclockwise • counterclockwise, clockwise • clockwise, clockwise • counterclockwise, counterclockwise • no current is induced

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