1. 1 Chapter 19: Magnetism The nature of magnetism Iron ore found near Magnesia Compass needles align N-S: magnetic Poles North (South) Poles attracted to geographic North (South) Like Poles repel, Opposites Attract No Magnetic Monopoles Define magnetic field lines = direction of compass deflection. Electric Currents produce deflections in compass direction. Electric Currents interact magnetically II I I FF F F

2. 2 Magnetic Fields in analogy with Electric Fields Electric Field: –Distribution of charge creates an electric field E in the surrounding space. –Field at charges location exerts a force F=q E on a charge q Magnetic Field: –Moving charge or current creates a magnetic field B in the surrounding space. –Field exerts a force F on a charge moving q F = qvB sin  is angle between B and v. –F is perpendicular to B an v

3. 3 F = |q| v B sin  = |q| v B (v  B) v B F + F = |q| v B sin  F = |q| v  B vv B F + v F = |q| v B sin  F = |q| v B  v B F + BB Right Hand Rule (1-2-3) : v, B, F

4. 4 Units of Magnetic Field Strength: [B]= [F]/([q][v]) = N/(C m s -1 ) = Tesla actually defined in terms of force on standard current CGS Unit 1 Gauss = 10 -4 Tesla Earth's field strength ~ 1 Gauss Direction = direction of velocity which generates no force

5. 5 J. J. Thomson’s Measurement of e/m Electron Gun   E V Example 19.2: Electrons are accelerated through a potential difference of 1000 V. The electrons then enter a region where there is a magnetic field and a “crossed” electric field (E and B are perpendicular), both of which are perpendicular to the beam. What magnitude magnetic field must be applied to exactly cancel the effect of the Electric field of 10 4 V/m?

6. 6 Field of a long straight wire s I B Magnetic field circulates around the wire; use Right hand rule for direction Thumb in direction of the current, fingers curl around in direction of B Example 19.2: Find the magnetic field 10 mm from a wire that carries a current of 1.0 A.

7. 7

8. 8 Fields tend to cancel in region right between wires. Field Lines continue down center of cylinder Field is negligible directly outside of the cylinder I B Magnetic Field in a Solenoid Close packed stacks of coils form cylinder B I

9. 9 Example 19.3: A solenoid 20 cm long and 40 mm in diameter with an air core is wound with a total of 200 turns of wire. The solenoid is to be used to exactly cancel the Earth's magnetic field where it is 3.0x10-5 T in magnitude. What should the current in the solenoid be for its field to exactly cancel the earth’s field inside the solenoid?

10. 10 Magnetic Materials Microscopic current loops: electron “orbits” electron “spin”  L  Quantum Effects: quantized angular momentum L, Pauli Exclusion Principle, etc. are important in macroscopic magnetic behavior.

11. 11 Magnetic Materials: Microscopic magnetic moments interact with an external (applied) magnetic field and each other, producing additional contributions to the net magnetic field B. Types of Materials Diamagnetic: Magnetic field decreases in strength. Paramagnetic: Magnetic field increases in strength. Ferromagnetic: Magnetic field increases in strength! Diamagnetic and Paramagnetic are often approximately linear with a relative permeability K M,  = K M  0

12. 12 Ferromagnetism: Greatly increases field Highly nonlinear, with Hysteresis: Hysteresis= magnetic record Magnetization forms in Magnetic Domains Saturation Permanent Magnetization B net BoBo

13. 13 More on the magnetic force on a moving charge For a charged particle moving perpendicular to the Magnetic Field + + v F F v –Circular Motion!

14. 14 Example 19.5 A mass spectrometer: velocity selector + circular trajectory   E R1R1 R2R2 E = 40.0 kV/m B =.0800 T Velocity Selector: uses crossed E and B, so that Electric and Magnetic Forces cancel for a particular velocity. (a)What is the speed of the ions pass through the velocity selector? (b) If the radius of the path of the ions is 390 mm, what is the mass of the ions?

15. 15 In a non-uniform field: Magnetic Mirror Net component of force away from concentration of field lines. B v F Magnetic Bottle Van Allen Radiation Belts

16. 16 Magnetic Force on a Current Carrying Wire vdvd I LL B FiFi A

17. 17 Example 19.6 (almost) A wire carries 100 A due west, suspended between two poles 50 m apart. The Earth’s field is 5.0 x 10 -5 T, directed north. What is the magnitude and direction of the magnetic force on the wire.

18. 18 Force between two long parallel current carrying wires (consider, for this example, currents in the same direction) I1I1 I2I2 B due to I 2 F due to I 2 F 12 = I 1 B due to I 2  L = I 1 (  o I 2 /(2  r)) L F/L =  o I 1 I 2 /(2  r) force on I 1 is towards I 2 force is attractive (force is repulsive for currents in opposite directions!) Example: Two 1m wires separated by 1cm each carry 10 A in the same direction. What is the force one wire exerts on the other

19. 19 Torque on a Current Loop (from force on wire segments) Rectangular loop in a magnetic field (directed along z axis) short side length a, long side length b, tilted with short sides at an angle with respect to B, long sides still perpendicular to B. B FaFa FaFa FbFb FbFb Forces on short sides cancel: no net force or torque. Forces on long sides cancel for no net force but there is a net torque.

20. 20 Torque calculation: Side view F b = IBb FbFb  moment arm a/2 cos   = F b a/2 cos  F b a/2 cos   Iab B cos  = I A B cos   I N A B cos  with N loops Magnetic Dipole ~ Electric Dipole Switch current direction every 1/2 rotation => DC motor Torque for armature of Galvanometer  magnetic moment  B

21. 21 Magnetic Poles: Magnetic “dipoles” from electric current No isolate magnetic poles, they are always present in pairs! No magnetic monopoles!