Magnetism

1. Magnetism Chapter 28

2. Chapter 28 Magnetic Fields In this chapter we will cover the following topics: Magnetic field vector Magnetic force on a moving charge Magnetic field lines Motion of a moving charge particle in a uniform magnetic field Magnetic force on a current carrying wire Magnetic torque on a wire loop Magnetic dipole, magnetic dipole moment Hall effect Cyclotron particle accelerator (28 – 1)

3. Magnetism was known long ago.

4. New Concept The Magnetic Field • We give it the symbol B. • A compass will line up with it. • It has Magnitude and direction so it is a VECTOR. • There are some similarities with the Electric Field but also some significant differences.

5. (28 – 2)

6. Magnetism • Refrigerators are attracted to magnets!

7. Where is Magnetism Used?? • Motors • Navigation – Compass • Magnetic Tapes • Music, Data • Television • Beam deflection Coil • Magnetic Resonance Imaging • High Energy Physics Research

8. Cathode Anode (28 – 8)

9. Magnet Demo – Compare to Electrostatics N S Magnet What Happens?? Pivot

10. Results - Magnets • Like Poles Repel • Opposite Poles Attract • Magnetic Poles are only found in pairs. • No magnetic monopoles have ever been observed. S N Shaded End is NORTH Pole Shaded End of a compass points to the NORTH.

11. Magnets Magnetic Field Cutting a bar magnet in half produces TWO bar magnets, each with N and S poles.

12. N S Consider a Permanent Magnet The magnetic Field B goes from North to South.

13. N N S S Introduce Another Permanent Magnet pivot The bar magnet (a magnetic dipole) wants to align with the B-field.

14. N N S S Field of a Permanent Magnet The south pole of the small bar magnet is attracted towards the north pole of the big magnet. The North pole of the small magnet is repelled by the north pole of the large magnet. The South pole pf the large magnet creates a smaller force on the small magnet than does the North pole. DISTANCE effect. The field attracts and exerts a torque on the small magnet.

15. N S N S Field of a Permanent Magnet The bar magnet (a magnetic dipole) wants to align with the B-field.

16. Convention For Magnetic Fields B X  Field INTO Paper Field OUT of Paper

17. Typical Representation

18. Experiments with Magnets Show • Current carrying wire produces a circular magnetic field around it. • Force (actually torque) on a Compass Needle (or magnet) increases with current.

19. B Current Carrying Wire Current into the page. Right hand Rule- Thumb in direction of the current Fingers curl in the direction of B

20. Current Carrying Wire • B field is created at ALL POINTS in space surrounding the wire. • The B field has magnitude and direction. • Force on a magnet increases with the current. • Force is found to vary as ~(1/d) from the wire.

21. Compass and B Field • Observations • North Pole of magnets tend to move toward the direction of B while S pole goes the other way. • Field exerts a TORQUE on a compass needle. • Compass needle is a magnetic dipole. • North Pole of compass points toward the NORTH.

22. Planet Earth

23. q • If the charge is moving, there • is a force on the charge, • perpendicularto both v and B. • F = q vxB q A Look at the Physics There is NO force on a charge placed into a magnetic field if the charge is NOT moving. There is no force if the charge moves parallel to the field.

24. The Lorentz Force This can be summarized as: F or: v q m B q is the angle between B and V

25. Nicer Picture

26. Another Picture

27. VECTOR CALCULATIONS

28. Practice B and v are parallel. Crossproduct is zero. So is the force. Which way is the Force???

29. Units

30. teslas are HUGE!

31. The Magnetic Force is Different From the Electric Force. Whereas the electric force acts in the same direction as the field: The magnetic force acts in a direction orthogonal to the field: (Use “Right-Hand” Rule to determine direction of F) And --- the charge must be moving !!

32. electron . . C r (28 – 9)

33. (28 – 10)

34. F Wires • A wire with a current contains moving charges. • A magnetic field will apply a force to those moving charges. • This results in a force on the wire itself. • The electron’s sort of PUSH on the side of the wire. Remember: Electrons go the “other way”.

35. (28 – 11)

36. The Wire in More Detail Assume all electrons are moving with the same velocity vd. L B out of plane of the paper

37. i . (28 – 12)

38. Current Loop What is force on the ends?? Loop will tend to rotate due to the torque the field applies to the loop.

39. Side view Top view C C (28 – 13)

40. (28 – 14)

41. R L L R L R (28 – 15)

42. The other sides t1=F1 (b/2)Sin(q) =(B i a) x (b/2)Sin(q) total torque on the loop is: 2t1 Total torque: t=(iaB) bSin(q) =iABSin(q) (A=Area)

43. Dipole Moment Definition • Define the magnetic • dipole moment of • the coil m as: • =NiA t=m X B We can convert this to a vector with A as defined as being normal to the area as in the previous slide.

44. Normal to the coil A Coil RIGHT HAND RULE TO FIND NORMALTO THE COIL: “Point or curl you’re the fingers of your right hand in the direction of the current and your thumb will point in the direction of the normal to the coil. Don't hurt yourself doing this!

45. An ApplicationThe Galvanometer

46. A 40.0-cm length of wire carries a current of 20.0 A. It is bent into a loop and placed with its normal perpendicular to a magnetic field with a magnitude of 0.520 T. What is the torque on the loop if it is bent into • an equilateral triangle? • What is the torque if the loop is • a square or • a circle? • Which torque is greatest?