# Magnetic Field and Magnetic Forces

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1 Chapter 27 Magnetic Field and Magnetic Forces PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson

2 Goals for Chapter 27 Magnets and the forces they exert on each other Force that a magnetic field exerts on a moving charge Magnetic field lines with electric field lines Motion of a charged particle in a magnetic field Applications of magnetism in physics and chemistry Magnetic forces on current-carrying conductors Current loops in a magnetic field

3 Introduction How does magnetic resonance imaging (MRI) allow us to see details in soft nonmagnetic tissue? How can magnetic forces, which act only on moving charges, explain the behavior of a compass needle? In this chapter, we will look at how magnetic fields affect charges.

4 Magnetic poles Forces between magnetic poles.

5 Magnetism and certain metals Either pole of a permanent magnet will attract a metal like iron.

6 Magnetic field of the earth and its field lines Why earth acts like a magnet? Walk around with a compass. What is a compass?

7 Magnetic monopoles Breaking a bar magnet does not separate its poles. There is no experimental evidence for magnetic monopoles. Why?

8 Electric current and magnets In 1820, Hans Oersted discovered that a current-carrying wire causes a compass to deflect. Seems like there is a connection between moving charge and magnetism.

9 The magnetic field A moving charge (or current) creates a magnetic field in the surrounding space. The magnetic field exerts a force on any other moving charge (or current) that is present in the field. Then force of the magnetic field changes the speed of the moving charges that in-turn creates a secondary magnetic field and Will come back to this later

10 The magnetic force on a moving charge

11 The magnetic force on a moving charge The magnetic force on q is perpendicular to both the velocity of q and the magnetic field. The magnitude of the magnetic force is F = q vb sinφ

12 Magnetic force as a vector product of v and B The right-hand rule gives the direction of the force on a positive charge.

13 Magnetic force as a vector product of v and B Direction of the magnetic force on a negative charge.

14 Equal velocities but opposite signs

15 Units of magnetic field B F = qv B N = C m s unit of B The SI unit of magnetic field B is tesla: 1 T = 1 N A m = 1 N C m / s Another unit is the gauss : 1 G = 10 4 T Gaussmeters : instruments measuring the magnetic field Magnetic field of the earch is of the order of 1G or 10 4 T Largest B field produced int the lab: 45T continuous & 120T (pulsed ms) B of a surface of a neutron star 10 8 T

16 Determining the direction of a magnetic field A cathode-ray tube can be used to determine the direction of a magnetic field.

17 Problem-Solving Strategy 27.1 Magnetic Forces

18 Magnetic force on a proton Example 27.1 A beam of protons move with speed of 3.0E5m/s on x-z plane at an angle 30 degrees with respect to +z axis through a uniform B-field of 2.0T along positive z-direction. Find the force on the proton magnitude and direction

19 Magnetic field lines

20 Magnetic field lines are not lines of force

21 Magnetic flux and magnetic Gauss s law We define the magnetic flux through a surface just as we defined the electric flux. Magnetic Gauss s law: The magnetic flux through any closed surface is zero. Φ B = B da = BcosΦdA = B da Magnetic flux through a closed surface : B da = 0 Magnetic field or magnetic flux density B = dφ B da

22 Units of magnetic flux Φ B = B A 1weber = 1T 1m 2 = 1N m A 1Wb = 1T m 2

23 Magnetic flux calculations Example 27.2: Area is 3.0cm 2 in a uniform B-field. Magnetic flux through the surface is 0.90mWb. Calculate the magnitude magnetic field. What is the direction of the area vector

24 Motion of charged particles in a magnetic field A charged particle in a magnetic field always moves with constant speed. If the velocity of the particle is perpendicular to the magnetic field, the particle moves in a circle of radius R = mv/ q B. The number of revolutions of the particle per unit time is the cyclotron frequency. Why path of the electron beam glows in this picture?

25 Helical motion If the particle has velocity components parallel to and perpendicular to the field, its path is a helix. The speed and kinetic energy of the particle remain constant.

26 Problem-Solving Strategy: Motion in Magnetic Fields

27 Magnetron inside a microwave oven Magnetron inside a microwave oven accelerates electrons. Accelerated charges emit radiation MHz is the frequency of rotation of electrons that leads to 2450 MHz frequency of microwave radiation.

28 Moving charged particle in a uniform magnetic field Example 27.3 A magnetron in a microwave oven emits EM waves with frequency 2450 MHz. What magnetic field strength is required for electrons to move in a circular path with this frequency?

29 Moving charged particle in a uniform magnetic field Example 27.4: In this figure the charged particle is proton and the T uniform magnetic field is along the x-axis. At t=0 the proton s velocity is (1.50E5m/s, 0m/s,2.00E5m/s). Find: the force on proton acceleration of the proton. radius of the helical path angular speed of the proton pitch of the helix

30 A nonuniform magnetic field Charges trapped in a magnetic bottle, which results from a non-uniform magnetic field. Used for containing ionized gas at high temperatures that any container will melt. Applications in fusion reactors that produces energy by colliding very high energy plasma and fusion reaction.

31 Bubble chamber (1952 by Donald A. Glaser) A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. In a pair production experiment high energy gamma rays hit hydrogen atoms and the tracks of charged particles in a bubble chamber curl under influence of a magnetic field

32 A nonuniform magnetic field The Van Allen radiation belts and the resulting aurora borealis (north wind) and aurora australis. These belts are due to the earth s nonuniform magnetic field.

33 Velocity selector A velocity selector uses perpendicular electric and magnetic fields to select particles of a specific speed from a beam. What is the velocity of the undeflected particles?

34 Thomson s e/m experiment Thomson s experiment measured the ratio e/m for the electron. His apparatus is shown in Figure below.

35 An e/m experiment 27.5 In a Thomson experiment the accelerating potential is 150 V and a deflecting electric field is 6.0E6N/C a) At what fraction of speed of light do the electrons move? b) What magnitude of the magnetic field you would need? c) With this magnetic field what will happen to the electron beam if you increase the accelerating potential above 150 V?

36 Mass spectrometer A mass spectrometer measures the masses of ions. The Bainbridge mass spectrometer first uses a velocity selector. Then the magnetic field separates the particles by mass.

37 The magnetic force on a current-carrying conductor Figure shows the magnetic force on a moving positive charge in a conductor. F = I l B df = Idl B

38 The magnetic force on a current-carrying conductor force is perpendicular to the wire segment and the magnetic field.

39 Loudspeaker Figure shows a loudspeaker design. If the current in the voice coil oscillates, the speaker cone oscillates at the same frequency.

40 Magnetic levitation What is the direction of the magnetic field if we want to levitate a current carrying rod horizontally? Current is flowing from right to left.

41 Magnetic force on a straight conductor Example 27.7 A straight horizontal copper rod carries a current of 50.0A between poles of a large magnet 1.20T as shown. a) Find the magnitude and direction of the force on a one meter section of the rod. b) While keeping the rod horizontal how should it be oriented to maximize the magnitude of the force? What is the force magnitude in this case.

42 Magnetic force on a curved conductor Example 27.8 The B-field is uniform as shown. The wire has a segment sticking out of the plane with current direction into the page and the curved part and straight part again. Find the total magnetic force on these segments of wire.

43 Force and torque on a current loop

44 Force and torque on a current loop The net force on a current loop in a uniform magnetic field is zero. But the net torque is not, in general, equal to zero.

45 Magnetic moment The right-hand rule to determine the direction of the magnetic moment of a current loop. µ = I A magnetic dipole moment Torque on a current loop or magnetic dipole τ = µbsinφ τ = µ B Potential energy for a magnetic dipole U = µib = µbcosφ

46 Magnetic torque and potential energy of a coil Example 27.9 circular coil of m radius with 30 turns in a horizontal plane. It carries a current of 5.00 A in a counterclockwise viewed from above located in a uniform magnetic field of 1.20T to the right. Find the magnetic moment and torque If the coil rotates from its original position to a position where the magnetic moment is parallel to B what is the change in potential energy?

47 How magnets work Follow the discussion in the text of magnetic dipoles and how magnets work. Use Figures (below) and (right).

48 The direct-current motor Follow the discussion in the text of the direct-current motor. Use Figures (right) and (below). Follow Example

49 The Hall Effect Follow the discussion of the Hall effect in the text using Figure below. Follow Example

50 Q27.1 A beam of electrons (which have negative charge q) is coming straight toward you. You put the north pole of a magnet directly above the beam. The magnetic Bfield from the magnet points straight down. Which way will the electron beam deflect? A. upward B. downward C. to the left D. to the right E. It won t deflect at all. N B Beam of electrons coming toward you

51 Q27.2 When a charged particle moves through a magnetic field, the direction of the magnetic force on the particle at a certain point is A. in the direction of the magnetic field at that point. B. opposite to the direction of the magnetic field at that point. C. perpendicular to the magnetic field at that point. D. none of the above E. The answer depends on the sign of the particle s electric charge.

52 Q27.3 A particle with a positive charge moves in the xz-plane as shown. The magnetic field is in the positive z-direction. The magnetic force on the particle is in A. the positive x-direction. B. the negative x-direction. C. the positive y-direction. D. the negative y-direction. E. none of these

53 Q27.4 A particle with charge q = 1 C is moving in the positive z-direction at 5 m/s. The magnetic field at its position is B = 3iˆ 4 ˆj T ( ) What is the magnetic force on the particle? A. B. C. D. ( iˆ + ˆj ) N ( iˆ ˆj ) ( iˆ + ˆj ) ( iˆ ˆj ) N N N E. none of these

54 Q27.5 A positively charged particle moves in the positive z-direction. The magnetic force on the particle is in the positive y-direction. What can you conclude about the x-component of the magnetic field at the particle s position? A. B x > 0 B. B x = 0 C. B x < 0 D. not enough information given to decide

55 Q27.6 A positively charged particle moves in the positive z-direction. The magnetic force on the particle is in the positive y-direction. What can you conclude about the y-component of the magnetic field at the particle s position? A. B y > 0 B. B y = 0 C. B y < 0 D. not enough information given to decide

56 Q27.7 A positively charged particle moves in the positive z-direction. The magnetic force on the particle is in the positive y- direction. What can you conclude about the z-component of the magnetic field at the particle s position? A. B z > 0 B. B z = 0 C. B z < 0 D. not enough information given to decide

57 Q27.8 Under what circumstances is the total magnetic flux through a closed surface positive? A. if the surface encloses the north pole of a magnet, but not the south pole B. if the surface encloses the south pole of a magnet, but not the north pole C. if the surface encloses both the north and south poles of a magnet D. none of the above

58 Q27.9 When a charged particle moves through a magnetic field, the trajectory of the particle at a given point is A. parallel to the magnetic field line that passes through that point. B. perpendicular to the magnetic field line that passes through that point. C. neither parallel nor perpendicular to the magnetic field line that passes through that point. D. any of the above, depending on circumstances.

59 Q27.10 A charged particle moves through a region of space that has both a uniform electric field and a uniform magnetic field. In order for the particle to move through this region at a constant velocity, A. the electric and magnetic fields must point in the same direction. B. the electric and magnetic fields must point in opposite directions. C. the electric and magnetic fields must point in perpendicular directions. D. The answer depends on the sign of the particle s electric charge.

60 Q27.11 A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic force on the loop is A. perpendicular to the plane of the loop, in a direction given by a right-hand rule. B. perpendicular to the plane of the loop, in a direction given by a left-hand rule. C. in the same plane as the loop. D. zero. E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.

61 Q27.12 A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the net magnetic torque on the loop A. tends to orient the loop so that its plane is perpendicular to the direction of the magnetic field. B. tends to orient the loop so that its plane is edge-on to the direction of the magnetic field. C. tends to make the loop rotate around its axis. D. is zero. E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.

### Q27.1 When a charged particle moves near a bar magnet, the magnetic force on the particle at a certain point depends

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