LECTURE 14 MAGNETIC FIELDS & FORCES

Transcription

1 LECTURE 14 MAGNETIC FIELDS & FORCES

2 Lecture 14 2 Reading chapter 26-1 to 26-2 Magnetic fields and force Motion of a point charge in a B field n Cyclotron motion n Velocity selector n q/m measurement for electrons n Mass spectrometer n Cyclotron

3 Demo: 1 3 Magnets on turntable Like poles repel, and unlike poles attract. This is not the electric force, and the ends of the magnet are not electrically charged. This force is the magnetic force.

4 Magnetic dipoles 4 Magnets have two magnetic poles: a north pole and a south pole. North and south poles always come in pairs. If a magnet is broken in half, each half has two poles. Magnets have only been observed to exist as a combined north and south pole, there are no isolated magnetic charges equivalent to the positive and negative charge.

5 Magnetic poles 5 Magnets have two magnetic poles: a north pole and a south pole. North and south poles always come in pairs. We have not seen a magnetic monopole, a north or south pole by itself. On Valentine s day, 1982, there was one candidate monopole observed, but this has never been reproduced. Phys. Rev. Lett

6 Magnetic fields 6 Magnetic field is the thing that transmits the magnetic force. A magnetic field surrounds every moving charged object. The existence of a magnetic field means that if an appropriate moving charged object is nearby, it will experience a force. An magnetic field is the possibility of a magnetic force. The unit of magnet field, B, is called the tesla, T, which is equivalent to N/(A m). Another common unit of magnetic field is the gauss, G. 1 T = 10 4 G

7 Magnetic field lines 7 Magnetic fields are visualized by magnetic field lines. Magnetic field lines always make complete loops. They neither begin nor end. Field lines never cross. By definition, magnetic field lines exit from the north pole of a magnet and enter at the south pole. The density of field lines indicate the magnitude of the field. Iron filings sprinkled around a bar magnet align themselves with the magnetic field.

8 Force by a magnetic field 8 The magnetic force on a moving charged particle is given by F = qv B and F = qv B sinθ θ is the angle between the magnetic field and the velocity of the charged particle. The direction of the magnetic force is always perpendicular to both velocity and the B field. Magnetic forces on point charges do no work.

9 Example: 1 9 An alpha particle (charge q = C and mass m = kg) travels at a velocity, v, of magnitude 550 m/s through a uniform magnetic field, B, of magnitude T. The angle between v and B is θ = 52. What are the magnitudes of a) the force acting on the particle due to the magnetic field? b) the acceleration of the particle due to the force? c) Does the speed of the particle change?

10 Demo: 2 10 Magnetic deflection Demonstration of an electron beam deflected by the magnetic field from a bar magnet

11 11 Quiz: 1

12 Thomson s q m measurement 12 J. J. Thomson discovered electrons and measured the q m ratio of electrons by shooting electrons in E and B fields. By tuning the B field, velocity of electrons were measured: v =. /. With the B field off, the amount of deflection depends on a = 1. 2.

13 Circular motion in magnetic fields 13 The magnetic force is always perpendicular to the velocity, therefore the particle undergoes uniform circular motion. If the magnetic field is also perpendicular to the velocity then 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: r = mv q B The period to complete a circle T (cyclotron period) and the orbital frequency f (cyclotron frequency) is independent of v or r and given by T = 1 f = 2πm qb

14 Demo: 3 14 Fine beam tube Demonstration of an electron beam bent into a circle by magnetic field r = mv q B

15 The mass spectrometer 15 The mass spectrometer measures masses of isotopes. Positive ions are accelerated through potential difference, ΔV. Ions enter the B field, and get deflected. m q = B2 r 2 2 ΔV

16 Particle identification 16 Bubbles form around the paths of particles in a bubble chamber (a vessel filled with a superheated liquid, often liquid hydrogen). The curvature depends on the momentum and the charge of the particle.

17 Helical motion 17 If the magnetic field is not perpendicular to the velocity, the component of velocity parallel to the B field does not change since there is no magnetic force along that direction. The particle moves in a helical path. The helical path of an electron in a cloud chamber (a vessel with a superheated vapor of water or alcohol).

18 Magnetic bottle 18 Magnetic field is stronger on both ends than in the middle. The particle spirals around the field lines and oscillates back and forth.

19 What causes aurora? 19 Charged particles ejected from the Sun (yellow and orange lines) are deflected by the Earths magnetic field (red lines) entering the Earths atmosphere at the north and south magnetic poles. The charged particles interact with the gas in the area to produce light.

20 Neutrino mass measurement 20 Electrons are emitted with velocities in all directions. A component along the B field and a component perpendicular to the B field. The perpendicular component causes it to travel in a circular path around the B field.

21 The cyclotron 21 Cyclotrons were invented to accelerate particles for studies of nuclei.

22 LHC (Large Hadron Collider) 22 LHC is the largest particle accelerator, synchrotron (27 km circumference). It speeds up and increases the energy of a beam of particles by generating electric fields that accelerate the particles, and magnetic fields that steer and focus them.