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   = BA cos  = BA  B =  0 nI = (4  X10 -7 )(1000)(10) = 0.0126 T  A = (0.1)(0.1) = 0.01 m 2

3. Current in Ring   = BA = (0.0126)(0.01) = 1.26 X 10 -4 Wb  In 1 second the flux goes to 0   = (1.26 X 10 -4 ) - (0) = 1.26 X 10 -4   t = 1   = -N(  /  t) = (1)(1.26 X 10 -4 ) = 1.26 X 10 -4 V   V = iR or i =  /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   = -N(d  /dt)  But the magnetic flux depends on the changing current and the properties of the coil   = -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   = L(di/dt) = N(d  /dt) L = N(d  /di)   Inductance is a property of the circuit element  Like resistance or capacitance

11. Solenoid Inductance  To find L, we need a relationship between  and I for a solenoid   Flux in general:   = BA cos  or  = BA   B =  0 (N/l)i or i = Bl/(  0 N)   L = N(d  /di) = N  /i = NBA  0 N/Bl =  0 N 2 A/l L =  0 n 2 Al  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. Motional emf - Derived  Consider a conductor of length L sliding on a frame with velocity v   but  x = v  t, so  A = Lv  t    /  t = B  A/  t = (BLv  t)/  t   = BLv X B field into page v x L  x in time  t AA

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 = i 2 R

17. Power and Motional emf  Since  = BLv and  = iR, we can write: i = BLv/R P = B 2 L 2 v 2 /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)? A)clockwise B)counterclockwise C)left D)right E)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? A)left B)right C)into the page D)out of the page E)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? A)clockwise, counterclockwise B)counterclockwise, clockwise C)clockwise, clockwise D)counterclockwise, counterclockwise E)no current is induced