Chapter 21

1. Chapter 21 Magnetic Induction February 20th, 2013

2. Review session for exam 1 Wednesday, Feb 20th, 4:35 PM, Chamberlin 3328, AbhishekAggarwal For the exam, bring a calculator, a pencil, and your “toolbox”, a single sheet of paper, on which you wrote BY HAND, front and back, all the formulas and information you may need. Everything else must be off the desk.

3. Demo Faraday’s Law magnetic flux ΦB= B A cosθ • A magnetic puck is dropped on a large copper plate. • As the magnet falls, it induces and emf (Faraday’s law) and therefore a current in the copper plate. • The induced current is called eddy current. • The eddy current generates a magnetic field, which opposes the motion of the puck (Lenz’s law). • Notice that the fall of the puck is slowed down by the eddy current. • If we cool the Cu plate in LN2 greater currents can flow through it, thus the puck falls more slowly 3

4. Demo Faraday’s Law magnetic flux ΦB= B A cosθ • A non-magnetic sphere is dropped through a copper (Cu) tube. Nothing special happens, no eddy currents induced, the sphere drops quickly • A magnetic sphere is dropped through the same copper tube. The moving magnet induces an emf, and therefore an eddy current in the Cu tube, and therefore a magnetic field opposing the fall of the magnet: the sphere drops slowly.

5. Demo Faraday’s Law magnetic flux ΦB= B A cosθ • A magnet rolls down an inclined aluminum (Al) track • The moving magnet induces emf, and eddy currents in both sides of the Al track • The resulting magnetic fields oppose the fall of the magnet • Therefore the magnet rolls down slowly

6. Demo Faraday’s Law magnetic flux ΦB= B A cosθ • A copper (Cu) plate is attached to strings so it can swing, like a pendulum. • The copper plate swings rapidly between two iron (Fe) red bars • Two electromagnets are present, each formed by a coil of wire around an Fe core, and more Fe components are positioned on top (all painted red). • When a switch is closed and current flows through the coils, a magnetic field is applied across the two Fe red bars. • The magnetic field induces eddy currents in the swinging Cu plate • The Cu plate comes to a slow stop • A Cu comb-shaped plate (right) continues to swing unaffected by the magnetic field, because no eddy currents can flow across comb teeth

7. RL Circuit

8. RL Circuit • DC circuits may contain resistors, inductors, and capacitors. The presence of R and L only makes a circuit an RL circuit • The voltage source is a battery or some other source that provides a constant voltage across its output terminals • Behavior of DC circuits with inductors • Immediately after any switch is closed or opened, the induced emfs keep the current through all inductors equal to the values they had the instant before the switch was thrown • After a switch has been closed or opened for a very long time, the induced emfs are zero

9. Time Constant for RL Circuit • The current at time t is found by • τ = time constant of the RL circuit • For 1R in series with 1L, τ= L / R • The voltage across the L VL= V e-t/τ

10. Problem 21.38

11. Problem 21.38, cont.

12. Real Inductors • Most practical inductors are constructed by wrapping a wire coil around a magnetic material • Filling a coil with magnetic material greatly increases the magnetic flux through the coil and therefore increases the induced emf • The presence of magnetic material increases the inductance • Most inductors contain a magnetic material inside which produces a larger value of L in a smaller package

13. Energy in an Inductor • Energy is stored in the magnetic field of an inductor • The energy stored in an inductor is PEind = ½ L I2 • Very similar in form to the energy stored in the electric field of a capacitor • The expression for energy can also be expressed as • In terms of the magnetic field,

14. Energy in an Inductor, cont. • Energy of the magnetic field actually exists everywhere there is a magnetic field, not just in a solenoid • Can also exist in “empty” space • The potential energy can also be expressed in terms of the energy density in the magnetic field • This expression is similar to the energy density contained in an electric field

15. Bicycle Odometers • An odometer measures the distance traveled • A permanent magnet is attached to a wheel • A pickup coil is mounted on the axle support • When the magnet passes over the pickup coil, a pulse is generated • A computer keeps track of the number of pulses

16. Ground Fault Interruptors (GFI) • A GFI is a safety device used in many household circuits • It uses Faraday’s Law along with an electromechanical relay • The relay uses the current through a coil to exert a force on a magnetic metal bar in a switch • During normal operation, there is zero magnetic field in the relay • If the current in the return coil is smaller, a non-zero magnetic field opens the relay switch and the current turns off

17. Electric Guitars • An electric guitar uses Faraday’s Law to sense the motion of the strings • The string is made of steel, which is ferromagnetic • Very near the string is a pickup coil, wound around a permanent magnet • This magnet magnetizes the nearby region of the string • As the string vibrates, it produces a changing magnetic flux through the pickup coil • The resulting emfinduced in the coil is sent to an amplifier and the signal can be played through speakers Mick Jagger Jimi Hendrix

18. Generators, Motors and Cars • Motors and generators provide examples of conservation of energy and the conversion of energy from one type to another • A hybrid car contains two motors and a generator • The hybrid car captures energy normally lost to heat and stores it in batteries • Still not a perfect conversion

19. Induction from a Distance • Assume a very long solenoid is inserted at the center of a single loop of wire • This will produce mutual inductance • The field from the solenoid at the outer loop is essentially zero

20. Induction from a Distance, cont. • The field inside the solenoid at the center of the loop still produces a magnetic flux through the inner portion of the loop • Energy is transferred across the empty space between the two conductors • The energy is carried from the solenoid to the outer loop by an electromagnetic wave