1. Physics 014
Magnetic Fields

2. Topics Definition of B Circulating charged particles
Force on a current carrying wire
Torque on a current loop
Magnetic dipole moments

4. B field Charges interact with electric fields but how do magnets work?
The magnetic field (B)

5. B field For the electric field Electric charges
Field everywhere in space

6. B field For the magnetic field Magnetic charges ? - NO
Field everywhere ? - YES

7. B field No magnetic charges (magnetic monopoles)
magnetic fields do effect charged particles

9. B field
The force on a particle with charge q and velocity v in a fields B and E is

10. B field
The SI unit for B is the tesla
1 tesla = 1 T =1 N/ (A m)

11. B field Another unit for B that is sometimes used is the guass
1 tesla = 104 gauss

12. B field
How do you find the force on a particle?

13. B field
How do you find the force on a particle?

14. ???
A charged particle with velocity v travels through a uniform field B. What is the direction of the magnetic force FB on the particle?

15. B field
Just as with the electric field, magnetic fields may be described by using field lines.

16. B field
Magnetic field lines

17. B field
Opposite poles attract, like repel

18. Circulating charges
If a charged particle enters a uniform B field with a velocity perpendicular to the field, it will move in a circle.

19. Circulating charges

22. Circulating charges
If particles are moving in a circle, the centripetal force is the magnetic force

23. Circulating charges
For the period and frequency of the charge

24. ???
For two particles (one proton the other an electron) traveling on circular paths each with the same speed in a uniform B field, which particle follows the smaller circle?

25. Force on a wire
We’ve seen that magnetic fields exert forces on charged particles. They also exert forces on wires.

26. Force on a wire

27. Force on a wire
In general, for a wire segment L , with current i and in a field B,

28. ???
The figure shows a current i through a wire in a uniform magnetic field B and the force on the wire FB. The field is oriented so that the force is maximum. In what direction is the field?

29. Torque on current loop
Consider what happens to a loop of current in a uniform magnetic field.

31. Torque on current loop
Consider a rectangular loop of length a and width b carrying a current i, in a uniform magnetic field B. What is the torque that causes the loop to rotate?

33. Torque on current loop Forces due to sides 2 and 4 cancel out
Sides 1 and 3 are perpendicular to B and yield a net torque

34. Torque on current loop
If instead of one loop we had a coil of N loops,

35. Magnetic Dipole Moment
We’ve seen that torque will rotate a coil in a uniform magnetic field.
The current loop acts like a bar magnet and is said to be a magnetic dipole

36. Magnetic Dipole Moment
Define the magnitude of the magnetic dipole moment (μ) as

37. Magnetic Dipole Moment
The direction of the magnetic dipole moment is found with the right hand rule.

38. Magnetic Dipole Moment
The torque on a current loop is then

39. Magnetic Dipole Moment
The magnetic potential energy of the magnetic dipole in an external field is

40. Magnetic Dipole Moment
Lowest energy = - μB
Highest energy = μB

41. Magnetic Dipole Moment
The work done on the dipole by the external field is

42. Magnetic Dipole Moment
The work done by an external agent is the negative of the work done by the field. (dipole stationary before and after change)

43. ???
For four orientations at angle θ of a magnetic dipole moment μ, rank the orientations according to (a) the magnitude of the torque on the dipole (b) the potential energy of the dipole, greatest first.