General Physics (PHYS )

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1 General Physics (PHYS ) Chapter 22 Magnetism Magnetic Force Exerted on a current Magnetic Torque Electric Currents, magnetic Fields, and Ampere s Law Current Loops and Solenoids Magnetism in Matter

2 Magnetism Magnetic effects from natural magnets have been known for a long time. Recorded observations from the Greeks more than 2500 years ago. The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece. Properties of lodestones: could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched. Small sliver of lodestone suspended with a string will always align itself in a north-south direction it detects the earth s magnetic field.

3 The Magnetic Field Permanent bar magnets have opposite poles on each end, called north and south. Like poles repel; opposites attract. If a magnet is broken in half, each half has two poles:

4 Bar Magnet Bar magnet... two poles: N and S Like poles repel; Unlike poles attract. Magnetic Field lines: (defined in same way as electric field lines, direction and density) S N Does this remind you of a similar case in electrostatics?

5 Electric Field Lines of an Electric Dipole Magnetic Field Lines of a bar magnet S N

6 Chapter 22 Cont. Magnetism 0/03/30/some-statistics-on-the-mcat-andyour-undergraduate-major/

7 Earth s Magnetic Field

8 Magnetic Monopoles? 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: S N S N S N 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! Even an individual electron has a magnetic dipole!

9 Source of Magnetic Fields? 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)

10 Magnetic Fields in analogy with Electric Fields Electric Field: Distribution of charge creates an electric field E(r) in the surrounding space. Field exerts a force F=q E(r) on a charge q at r Magnetic Field: Moving charge or current creates a magnetic field B(r) in the surrounding space. Field exerts a force F on a charge moving q at r (emphasis this chapter is on force law) 11

11 Applications of magnetic forces electric motor, electric car, electric generator, electric drill, solenoid actuator. tape recorder, magnetic hard drive, CRT for oscilloscopes and TV magnetic levitation for trains science (Nmr, mass spectrometer) medicine (MRI; magnetic navigation systems for catheter)

12 The Magnetic Force on Moving Charges This is an experimental result we observe it to be true.

13 Force on a Charge Moving in a Magnetic Field B F B q v B is the magnetic force is the charge is the velocity of the charge is the magnetic field This equation defines B, just as qe defines. F E E

14 Magnitude of F B. The magnitude of F B = q v B sin q q is the smaller angle between v and B F B is zero when and are parallel or antiparallel q = 0 or 180 o F B is a maximum when and are perpendicular q = 90 o v v B B

15 The Magnetic Force on Moving Charges The magnetic force on a moving charge is actually used to define the magnetic field:

16 Recall F qvbsin( q ) F so B qvsin( q ) The SI unit of magnetic field is the tesla (T). T C N ( m / s) N A m The gauss (G) is also a commonly used unit: 1 T = 10 4 G

17 So, we know how to find the magnitude. How do we find the direction of the magnetic force F?

18 Direction of F B : tricky because of cross product 19

19 The Magnetic Force on Moving Charges In order to figure out which direction the force is on a moving charge, you can use a right-hand rule. This gives the direction of the force on a positive charge.

20 Direction of F B : Right-Hand Rule #1 Your thumb is in the direction of the force if q is positive. 21

21 Left Hand Rule Left hand rule is used for electrons charges. Your turn how would it look like?

22 Got it 1 Figure shows a proton in a magnetic field. For which of the three proton velocities shown will the magnetic force be greatest? 1. a 2. b 3. c 4. none 0% 0% 0% 0%

23 Got it 2 Figure shows a proton in a magnetic field. What will be the direction of the force in all three cases? 1. Parallel into the paper 2. Parallel out of the paper 3. Perpendicular into the paper 4. Perpendicular out of the paper 0% 0% 0% 0%

24 Example 2 Figure shows 3 protons entering a 0.10-T magnetic field. All three are moving at 2.0 Mm/s. Find the magnetic force on each. B F q v B F B + F E = 0 when v = E/B Electromagnetic force velocity selector.

25 The Motion of Charged Particles in a Magnetic Field A positively charged particle in an electric field experiences a force in the direction of the field; in a magnetic field the force is perpendicular to the field. This leads to very different motions:

26 The Motion of Charged Particles in a Magnetic Field Because the magnetic force is always perpendicular to the direction of motion, the path of a particle is circular. Also, while an electric field can do work on a particle, a magnetic field cannot the particle s speed remains constant.

27 The Motion of Charged Particles in a Magnetic Field For a particle of mass m and charge q, moving at a speed v in a magnetic field B, the radius of the circle it travels is:

28 Charged particle in a magnetic field _wudblg8&list=plf7a98fe5f5d0b39d

29 GOT IT 3 A uniform magnetic field points out of this page. Will an electron that s moving in the plane of the page circle 1. Clockwise 2. Counterclockwise 0% 0% as viewed from above the page?

30 The Motion of Charged Particles in a Magnetic Field In a mass spectrometer, ions of different mass and charge move in circles of different radii, allowing separation of different isotopes of the same element.

31 The Motion of Charged Particles in a Magnetic Field If a particle s velocity makes an angle with the magnetic field, the component of the velocity along the magnetic field will not change; a particle with an initial velocity at an angle to the field will move in a helical path.

32 Aurora Borealis watch?v=lt3j6a9p_o8

33 The Magnetic Force Exerted on a Current- Carrying Wire The force on a segment of a current-carrying wire in a magnetic field is given by:

34 RHR and LHR can be used for other variables.

35 Demo

36 Summary of Chapter 22 All magnets have two poles, north and south. Magnetic fields can be visualized using magnetic field lines. These lines point away from north poles and toward south poles. The Earth produces its own magnetic field. A magnetic field exerts a force on an electric charge only if it is moving: A right-hand rule gives the direction of the magnetic force on a positive charge.

37 Summary of Chapter 22 If a charged particle is moving parallel to a magnetic field, it experiences no magnetic force. If a charged particle is moving perpendicular to a magnetic field, it moves in a circle: If a charged particle is moving at an angle to a magnetic field, it moves in a helix.

General Physics (PHYS )

General Physics (PHYS ) Chapter 21-22 Electricity and Magnetism Resistors in series and parallel Kirchoff s rules Magnetism Magnets Announcement Exam: Question # 11 & Last problem Science FunLand Volunteer