2. Units  Tesla (SI)  N/(Cm/s)  N/(Am)  Gauss  1 T = 10 4 gauss

3. Magnetic Dipole Magnetic Field (B)

4. Magnetic Monopoles  Do not exist!  In this way they differ from electric dipoles, which can be separated into electric monopoles.

5. Magnetic Force on Charged Particle n magnitude: F = qvBsin  –q: charge in Coulombs –v: speed in meters/second –B: magnetic field in Tesla –  : angle between v and B n direction: Right Hand Rule

6. Magnetic Force Calculate the magnitude and direction of the magnetic force. v = 300,000 m/s B = 200 mT q = 3.0  C 34 o

7. Magnetic Fields  Formed by moving charge  Affect moving charge

8. Magnetic Forces can... n accelerate charged particles by changing their direction n cause charged particles to move in circular or helical paths

9. Magnetic Forces cannot... n change the speed or kinetic energy of charged particles n do work on charged particles

10. When v and B are at right angles to each other... B V F V F V F V F qvBsin  = mv 2 /r qB = mv/r q/m = v/(rB)

11. Electric and Magnetic Fields Together E B v = E/B q

12. Magnetic Force on Current-carrying Wire n F = I L B sin  –I: current in Amps –L: length in meters –B: magnetic field in Tesla –  : angle between current and field

13. Magnetic Field for Long Straight Wire n B =  o I/(2  r)  o : 4   10 -7 Tm/A magnetic permeability of free space I: current (A) r: radial distance from center of wire (m)

14. Hand Rule n Curve your fingers n Place your thumb (which is presumably pretty straight) in direction of current. n Curved fingers represent curve of magnetic field. n Field vector at any point is tangent to field line. i r 

15. For straight currents I

16. Principle of Superposition vector addition When there are two or more currents forming a magnetic field, calculate B due to each current separately and then add them together using vector addition.

17. Beyond the 4th Grade I

18. Magnetic Field Inside a Solenoid n B =  o nI  o : 4   10 -7 Tm/A n: number of coils per unit length I: current (A)

19. Lab: Magnetic Field Map I Using a compass, map the magnetic field inside and outside your solenoid. Show the following: a)Tracing of solenoid (true size) b)Current through solenoid c)Connection to DC outlet d)Field lines mapped with compass e)Edge effects (What happens to those field lines farther away from the solenoid? Can you explain it?) f)North and South Poles of solenoid g)The Compass Rose h)One drawing per group (Write all names on paper)

20. Lab Evaluation Magnetic Field Map A) Are field lines visible in the core of the solenoid? B) Are the directions of the field lines in the core consistent with the Right Hand Rule? C) Are the North and South Poles correctly identified?

21. Magnetic Flux  The product of magnetic field and area.  Can be thought of as a total magnetic “effect” on a coil of wire of a given area.

22. Magnetic Flux   B = BAcos    B : magnetic flux in Webers (Tesla meters 2 )  B: magnetic field in Tesla  A: area in meters 2.   : the angle between the area and the magnetic field.

23. Magnetic Flux  A system will respond so as to oppose changes in magnetic flux.  Changing the magnetic flux can generate electrical current.

24. Faraday’s Law of Induction   = -N  B /  t   induced potential (V)  N: # loops   B : magnetic flux (Webers, Wb)  t: time (s)

25. A closer look …   = -  B /  t   = -  (BAcos  )/  t  To generate voltage  Change B  Change A  Change 

26. Lenz’s Law  The current will flow in a direction so as to oppose the change in flux.  Use in combination with hand rule to predict current direction.

27. Announcements –AP Review every morning at 7:00 AM. –Lunch Bunch tomorrow (come with pretest completed). –Exam Thursday –1988 AP Free Response: Thursday and Friday, after school or at lunch

28. Challenge Problem #3 How large a force is needed to move the rod at a constant speed of 2 m/s? How much power is dissipated in the resistor?       B = 0.15 T v = 2 m/s 50 cm 3 