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Inductors

Inductors. PH 203 Professor Lee Carkner Lecture 20. Ring in Solenoid. If the current flows clockwise through the solenoid, the B field inside is straight down To get maximum flux, the ring should face up (parallel with the coils)

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Inductors

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  1. Inductors PH 203 Professor Lee Carkner Lecture 20

  2. Ring in Solenoid • If the current flows clockwise through the solenoid, the B field inside is straight down • To get maximum flux, the ring should face up (parallel with the coils) • We need to find the flux through the loop before and after the current is switched off • F = BA cos q = BA • B = m0nI = (4pX10-7)(1000)(10) = 0.0126 T • A = (0.1)(0.1) = 0.01 m2

  3. Current in Ring • F = BA = (0.0126)(0.01) = 1.26 X 10-4 Wb • In 1 second the flux goes to 0 • DF = (1.26 X 10-4) - (0) = 1.26 X 10-4 • Dt = 1 • e = -N(DF/Dt) = (1)(1.26 X 10-4) = 1.26 X 10-4 V • DV = iR or i = e/R = 1.26 X 10-4/10 • i = 1.26 X 10-5 A

  4. Applied Induction • You connect a source of motion to a magnet • The changing flux produces a changing current • Can easily amplify and move the current • Many applications in music

  5. Microphone

  6. Electric Guitar

  7. Induction Devices • Microphone • Speaker • Electric guitar • Pickup magnet magnetizes string, the motion of which induces current • Tape recorders and players • The tape is magnetized such that when it passes the tape heads it induces a current

  8. How Does Induction Work? • If we move the wire through a B field the electrons now have a velocity • This deflection produces an imbalance of charge

  9. 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

  10. 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

  11. 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

  12. 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:

  13. 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?

  14. 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

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

  16. 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

  17. 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

  18. Force on Eddy Currents

  19. Eddy Currents • Imagine a loop moving out of a magnetic field • As the field through the loop drops, it induces a field in the same direction • If the object is not a loop, circular currents can still be induced which have the same effect • Called eddy currents • Metal objects moving through a magnetic field will be slowed

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

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

  22. 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

  23. 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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