1. Magnetic Fields

2. Magnetic Fields and Forces a single magnetic pole has never been isolated magnetic poles are always found in pairs Earth itself is a large permanent magnet

3. Magnetic Fields and Forces

4. We can represent the magnetic field ( ) by means of drawings with magnetic field lines We can define a magnetic field at some point in space in terms of the magnetic force that the field exerts on a charged particle moving with a velocity Magnetic poles exert attractive or repulsive forces on each other and that these forces vary as the inverse square of the distance between interacting poles

5. Magnetic Fields and Forces The magnitude F B of the magnetic force exerted on the particle is proportional to the charge q and to the speed v of the particle The magnitude and direction of depend on the velocity of the particle and on the magnitude and direction of the magnetic field (Tesla, T=N.s/(C.m), in SI unit) When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero

6. Magnetic Fields and Forces

8. Example #13 An electron in a television picture tube moves toward the front of the tube with a speed of 8.0 x10 6 m/s along the x axis (see the figure). Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude 0.025 T, directed at an angle of 60 0 to the x axis and lying in the xy plane. Calculate the magnetic force on the electron.

9. Magnetic Force Acting on a Current-Carrying Conductor The resultant force exerted by the field on the wire is the vector sum of the individual forces exerted on all the charged particles making up the current

10. Magnetic Force Acting on a Current-Carrying Conductor

12. n : the number of charges per unit volume

13. Magnetic Force Acting on a Current-Carrying Conductor

14. The magnetic force on a curved current- carrying wire in a uniform magnetic field is equal to that on a straight wire connecting the end points and carrying the same current

15. Magnetic Force Acting on a Current-Carrying Conductor The net magnetic force acting on any closed current loop in a uniform magnetic field is zero

16. Quiz#3 Rank the wires according to the magnitude of the magnetic force exerted on them, from greatest to least

17. Sources of the Magnetic Field The Biot–Savart Law  0 : 4 x 10 -7 T.m/A

18. Magnetic Field Surrounding a Thin, Straight Conductor

19. Magnetic Field on the Axis of a Circular Current Loop At x=0 If x>>R

20. Magnetic Field on the Axis of a Circular Current Loop

21. The Magnetic Force Between Two Parallel Conductors Parallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in opposite directions repel each other

22. Ampère’s Law

23. The line integral of around any closed path equals  0 I, where I is the total steady current passing through any surface bounded by the closed path

24. Quiz#4 Rank the magnitudes of for the closed paths in the figure from least to greatest

25. The Magnetic Field of a Solenoid A solenoid is a long wire wound in the form of a helix

26. The Magnetic Field of a Solenoid

27. From Ampère’s Law N: the number of turns n: the number of turns per unit length

28. Magnetic Flux

30. Gauss’s Law in Magnetism The net magnetic flux through any closed surface is always zero

31. The Magnetic Field of the Earth

32. Faraday’s Law of Induction An electric current can be induced in a secondary circuit by a changing magnetic field An induced emf is produced in the secondary circuit by the changing magnetic field The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit

33. Faraday’s Law of Induction a coil consisting of N loops all of the same area

34. Faraday’s Law of Induction

35. Lenz’s Law The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop

36. Lenz’s Law