1. Chapter 19: Magnetism Magnets  Magnets Homework assignment : 18,25,38,45,50 Read Chapter 19 carefully especially examples.

2.  Magnetic force Magnets

3.  Magnetic field lines Magnets

4.  Magnetic field lines Magnets

5.  Magnetic field lines (cont’d) Electric Field Lines of an Electric Dipole Magnetic Field Lines of a bar magnet

6.  Magnetic monopole? Magnets Many searches for magnetic monopoles—the existence of which would explain (within framework of QM) the quantization of electric charge (argument of Dirac) No monopoles have ever been found: Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or magnetic charge). How can you isolate this magnetic charge? Try cutting a bar magnet in half: NS NNSS Even an individual electron has a magnetic “dipole”!

7. Magnets  Source of magnetic field What is the source of magnetic fields, if not magnetic charge? Answer: electric charge in motion! e.g., current in wire surrounding cylinder (solenoid) produces very similar field to that of bar magnet. Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter. Orbits of electrons about nuclei Intrinsic “spin” of electrons (more important effect)

8. Magnets  Magnetic field of Earth The geographic North Pole corresponds a magnetic south pole. The geographic South Pole corresponds a magnetic north pole. The angle between the direction of the magnetic field and the horizontal is called the dip angle. The difference between true north and, defined as the geographic North Pole, and north indicated by a compass varies from point to point on Earth. This difference is referred to as a magnetic declination.

9. Magnetic Fields  Magnetic force: Observations vector product magnitude:

10. Magnetic Fields  Magnetic force (Lorentz force) SI unit : tesla (T) = Wb/m 2 right-hand rule

11. Magnetism  Magnetic force (cont’d) Units of magnetic field

12. Magnetic Fields  Magnetic force (Lorentz force) Magnetic force F x x x v B q  v B q F = 0  v B q F 

13.  Magnetic force on a current (straight wire) Magnetic Force on a Current-Carrying Conductor

14.  Magnetic force on a current (straight wire) (cont’d) Magnetic Force on a Current-Carrying Conductor

15.  Plane of loop is parallel to the magnetic field Force and Torque on a Current Loop  =rFsin 

16.  Plane of loop : general case Force and Torque on a Current Loop

17.  Plane of loop and magnetic moment

18.  Motor flip the current direction Force and Torque on a Current Loop

19.  Case 1: Velocity perpendicular to magnetic field Motion of Charged Particles in a Magnetic Field υ perpendicular to B The particle moves at constant speed υ in a circle in the plane perpendicular to B. F/m = a provides the acceleration to the center, so v R x B F

20.  Case 1: Velocity perpendicular to magnetic field (cont’d) Motion of Charged Particles in a Magnetic Field

21.  Case 1: Velocity perpendicular to magnetic field (cont’d) Motion of Charged Particles in a Magnetic Field Velocity selector

22.  Case 1: Velocity perpendicular to magnetic field (cont’d) Motion of Charged Particles in a Magnetic Field Mass spectrometer

23.  Case 1: Velocity perpendicular to magnetic field (cont’d) Motion of Charged Particles in a Magnetic Field Mass spectrometer

24.  Case 1: Velocity perpendicular to magnetic field (cont’d) Motion of Charged Particles in a Magnetic Field Mass spectrometer

25.  Case 1: Velocity perpendicular to magnetic field (con’t) Motion of Charged Particles in a Magnetic Field Mass spectrometer

26.  Case 2: General case Motion of Charged Particles in a Magnetic Field υ at any angle to B. Begin by separating the two components of υ into //          

27.  Case 2: General case (cont’d) Motion of Charged Particles in a Magnetic Field Since the magnetic field does not exert force on a charge that travels in its direction, the component of velocity in the magnetic field direction does not change.

28. Exercises  Exercise 1 If a proton moves in a circle of radius 21 cm perpendicular to a B field of 0.4 T, what is the speed of the proton and the frequency of motion? v r xx xx 1 2

29. Exercises  Exercise 2 Example of the force on a fast moving proton due to the earth’s magnetic field. (Already we know we can neglect gravity, but can we neglect magnetism?) Let v = 10 7 m/s moving North. What is the direction and magnitude of F? Take B = 0.5x10 -4 T and v  B to get maximum effect. (a very fast-moving proton) B N F v vxB is into the paper (west). Check with globe

30.  Magnetic field due to a long straight wire Iron filings Magnetic Field of a Long Straight Wire and Ampere’s Law Magnetic field by a long wire    x10 -7 T m/A permeability of free space right-hand rule 2

31.  Ampere’s (circular) law : A circular path Ampere’s Law Consider any circular path of radius R centered on the wire carrying current I. Evaluate the scalar product B·  s around this path. Note that B and  s are parallel at all points along the path. Also the magnitude of B is constant on this path. So the sum of all the    s terms around the circle is On substitution for B Ampere’s circuital law (valid for any closed path) ss ss ss ss amount of current that penetrates the loop

32.  Two parallel wires Force Between Parallel Conductors At a distance a from the wire with current I 1 the magnetic field due to the wire is given by d Force per unit length

33.  Two parallel wires (cont’d) Force Between Parallel Conductors Parallel conductors carrying current in the same direction attract each other. Parallel conductors carrying currents in opposite directions repel each other. d d

34.  Definition of ampere Force Between Parallel Conductors The chosen definition is that for d = L = 1m, The ampere is made to be such that F 2 = 2×10 −7 N when I 1 =I 2 =1 ampere This choice does two things (1) it makes the ampere (and also the volt) have very convenient magnitudes for every day life and (2) it fixes the size of μ 0 = 4π×10 −7. Note ε 0 = 1/(μ 0 c 2 ). All the other units follow almost automatically. d

35.  Magnetic field by a current loop Magnetic Fields of Current Loops and Solenoids   x1x1 x2x2 1)The segment  x 1 produces a magnetic field  magnitude B 1 at the center of the loop, directed out of the page. 2) The segment  x 2 produces a magnetic field  magnitude B 2 at the center of the loop, directed out of the page. The magnitude of B 1 and B 2 are the same. R The magnitude of the magnetic field at the center of a circular loop carrying current I The magnitude of the magnetic field at the center of N circular loops carrying current I

36. If d << L, the B field is to first order contained within the solenoid, in the axial direction, and of constant magnitude. In this limit, we can calculate the field using Ampere's law. L A solenoid is defined by a current i flowing through a wire that is wrapped n turns per unit length on cylinder of radius d and length L. d Magnetic Fields of Current Loops and Solenoids  Magnetic field by a solenoid Inside the solenoid, B is constant and outside it is zero in this approximation. Apply Ampere’s law to the rectangular loop represented by blue dashed lines. number of turn per unit length

37. The magnetic field of a solenoid is essentially identical to that of a bar magnet  Magnetic field by a solenoid (cont’d) solenoidbar magnet A mystery of : R x P I B field at point P: In a solenoid, the B field at its axis: