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Lecture 15

Lecture 15. Faraday’s Law Induction Motional EMF Generators Self Inductance. Faraday’s Law and Lenz’ Law. The change in the flux, ΔΦ B , can be produced by a change in B, A or θ Since Φ B = B A cos θ

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Lecture 15

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  1. Lecture 15 • Faraday’s Law Induction • Motional EMF • Generators • Self Inductance

  2. Faraday’s Law and Lenz’ Law • The change in the flux, ΔΦB, can be produced by a change in B, A or θ • Since ΦB = B A cos θ • The negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law • The current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit

  3. Lenz’ Law – Example • The magnetic field, , becomes smaller with time • This reduces the flux • The induced current will produce an induced field, ind, in the same direction as the original field

  4. Fig. 20-9b, p.666

  5. Applications of Faraday’s Law – Ground Fault Interrupters • The ground fault interrupter (GFI) is a safety device that protects against electrical shock • Wire 1 leads from the wall outlet to the appliance • Wire 2 leads from the appliance back to the wall outlet • The iron ring confines the magnetic field, which is generally 0 • If a leakage occurs, the field is no longer 0 and the induced voltage triggers a circuit breaker shutting off the current

  6. Fig. 20-9, p.666

  7. Fig. 20-CO, p.660

  8. Applications of Faraday’s Law – Electric Guitar • A vibrating string induces an emf in a coil • A permanent magnet inside the coil magnetizes a portion of the string nearest the coil • As the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coil • The changing flux produces an inducedemf that is fed to an amplifier

  9. Applications of Faraday’s Law – Apnea Monitor • The coil of wire attached to the chest carries an alternating current • An induced emf produced by the varying field passes through a pick up coil • When breathing stops, the pattern of induced voltages stabilizes and external monitors sound an alert

  10. Fig. P20-17, p.686

  11. Application of Faraday’s Law – Motional emf • A straight conductor of length ℓ moves perpendicularly with constant velocity through a uniform field • The electrons in the conductor experience a magnetic force • F = q v B • The electrons tend to move to the lower end of the conductor

  12. Motional emf • As the negative charges accumulate at the base, a net positive charge exists at the upper end of the conductor • As a result of this charge separation, an electric field is produced in the conductor • Charges build up at the ends of the conductor until the downward magnetic force is balanced by the upward electric force • There is a potential difference between the upper and lower ends of the conductor

  13. Motional emf, cont • The potential difference between the ends of the conductor can be found by • ΔV = B ℓ v • The upper end is at a higher potential than the lower end • A potential difference is maintained across the conductor as long as there is motion through the field • If the motion is reversed, the polarity of the potential difference is also reversed

  14. Motional emf in a Circuit • Assume the moving bar has zero resistance • As the bar is pulled to the right with a given velocity under the influence of an applied force, the free charges experience a magnetic force along the length of the bar • This force sets up an induced current because the charges are free to move in the closed path

  15. Fig. P20-63, p.691

  16. Fig. P20-64, p.691

  17. Motional emf in a Circuit, cont • The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop • The induced, motional emf, acts like a battery in the circuit

  18. Lenz’ Law Revisited – Moving Bar Example • As the bar moves to the right, the magnetic flux through the circuit increases with time because the area of the loop increases • The induced current must be in a direction such that it opposes the change in the external magnetic flux

  19. Lenz’ Law, Bar Example, cont • The flux due to the external field is increasing into the page • The flux due to the induced current must be out of the page • Therefore the current must be counterclockwise when the bar moves to the right

  20. Lenz’ Law, Bar Example, final • The bar is moving toward the left • The magnetic flux through the loop is decreasing with time • The induced current must be clockwise to to produce its own flux into the page

  21. Lenz’ Law – Moving Magnet Example • A bar magnet is moved to the right toward a stationary loop of wire (a) • As the magnet moves, the magnetic flux increases with time • The induced current produces a flux to the left, so the current is in the direction shown (b)

  22. Lenz’ Law, Final Note • When applying Lenz’ Law, there are two magnetic fields to consider • The external changing magnetic field that induces the current in the loop • The magnetic field produced by the current in the loop

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