普通物理 General Physics 28 - Magnetic Force 郭艷光Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件: ykuo@cc.ncue.edu.tw 網頁: http://ykuo.ncue.edu.tw

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Outline 28-1 What Is Physics? 28-2 What Produces a Magnetic Field? 28-3 The Definition of 28-4 Crossed Fields: Discovery of the Electron 28-5 Crossed Fields: The Hall Effect 28-6 A Circulating Charged Particle 28-7 Cyclotrons and Synchrotrons 28-8 Magnetic Force on a Current-Carrying Wire 28-9 Torque on a Current Loop 28-10 The Magnetic Dipole Moment 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 28-1 What Is Physics? As we have discussed, one major goal of physics is the study of how an electric field can produce an electric force on a charged object. A closely related goal is the study of how a magnetic field can produce a magnetic force on a (moving) charged particle or on a magnetic object such as a magnet. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-2 What Produces a Magnetic Field? One way is to use moving electrically charged particles, such as a current in a wire, to make an electromagnet. The other way to produce a magnetic field is by means of elementary particles such as electrons because these particles have an intrinsic magnetic field around them. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 28-3 The Definition of For all other directions FB is not zero and its magnitude where is the angle between v and B. SI unit of B: Tesla 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 28-3 The Definition of Vector product 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 28-3 The Definition of At any point P, the magnetic field vector is tangent to the magnetic field lines. The magnitude of the magnetic field vector is proportional to the density of the magnetic field lines. P Magnetic field line Magnetic field lines P Q 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-1 A uniform magnetic field , with magnitude 1.2 mT, is directed vertically upward throughout the volume of a laboratory chamber. A proton with kinetic energy 5.3 MeV enters the chamber, moving horizontally from south to north. What magnetic deflecting force acts on the proton as it enters the chamber? The proton mass is 1.67 × 1027 kg. (Neglect Earth’s magnetic field.) 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-1 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-4 Crossed Fields: Discovery of the Electron Cathode Anode J. J. Thomson in 1897 used a version of this tube to investigate the nature of the particle beam that caused the fluorescent spot. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-5 Crossed Fields: The Hall Effect In 1879, Edwin Hall: Conduction in metals is due to the motion of negative charges (electrons). 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-2 A solid metal cube, of edge length d = 1.5 cm, moving in the positive y direction at a constant velocity of magnitude 4.0 m/s. The cube moves through a uniform magnetic field of magnitude 0.050 T in the positive z direction. (a) Which cube face is at a lower electric potential and which is at a higher electric potential because of the motion through the field? (b) What is the potential difference between the faces of higher and lower electric potential? 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-2 The left face is at a lower electric potential, and the right face is at a higher electric potential. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-6 A Circulating Charged Particle . Electron C r 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-6 A Circulating Charged Particle 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-3 The essentials of a mass spectrometer, which can be used to measure the mass of an ion; an ion of mass m (to be measured) and charge q is produced in source S. The initially stationary ion is accelerated by the electric field due to a potential difference V. The ion leaves S and enters a separator chamber in which a uniform magnetic field is perpendicular to the path of the ion. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-3 A wide detector lines the bottom wall of the chamber, and the causes the ion to move in a semicircle and thus strike the detector. Suppose that B = 80.000 mT, V = 1000.0 V, and ions of charge q = 1.6022 × 1019 C strike the detector at a point that lies at x 1.6254 m. What is the mass m of the individual ions, in atomic mass units (Eq. 1-8: 1 u = 1.6605 × 1027 kg)? 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-3 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-4 An electron with a kinetic energy of 22.5 eV moves into a region of uniform magnetic field of magnitude 4.55 × 10-4 T. The angle between the directions of and the electron’s velocity is 65.5° What is the pitch of the helical path taken by the electron? 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-4 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-7 Cyclotrons and Synchrotrons The key to the operation of the cyclotron is that the frequency f at which the proton circulates in the magnetic field (and that does not depend on its speed) must be equal to the fixed frequency fosc of the electrical oscillator, or f= fosc (resonance condition). 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-7 Cyclotrons and Synchrotrons At proton energies above 50 MeV, the conventional cyclotron begins to fail because one of the assumptions of its design—that the frequency of revolution of a charged particle circulating in a magnetic field is independent of the particle’s speed—is true only for speeds that are much less than the speed of light. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-5 Suppose a cyclotron is operated at an oscillator frequency of 12 MHz and has a dee radius R = 53 cm. (a) What is the magnitude of the magnetic field needed for deuterons to be accelerated in the cyclotron? The deuteron mass is m = 3.34 × 1027 kg. (b) What is the resulting kinetic energy of the deuterons? 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-5 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-5 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-8 Magnetic Force on a Current-Carrying Wire 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-8 Magnetic Force on a Current-Carrying Wire . i 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-6 A straight, horizontal length of copper wire has a current i = 28 A through it. What are the magnitude and direction of the minimum magnetic field needed to suspend the wire—that is, to balance the gravitational force on it? The linear density (mass per unit length) of the wire is 46.6 g/m. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-6 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-9 Torque on a Current Loop 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-9 Torque on a Current Loop 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-7 Analog voltmeters and ammeters work by measuring the torque exerted by a magnetic field on a current-carrying coil. The reading is displayed by means of the deflection of a pointer over a scale. Figure 28-22 shows the essentials of a galvanometer, a device on which both analog ammeters and analog voltmeters are based. Assume the coil is 2.1 cm high and 1.2 cm wide, has 250 turns, and is mounted so that it can rotate about an axis (into the page) in a uniform radial magnetic field with B = 0.23 T. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-7 For any orientation of the coil, the net magnetic field through the coil is perpendicular to the normal vector of the coil (and thus parallel to the plane of the coil). A spring Sp provides a countertorque that balances the magnetic torque, so that a given steady current i in the coil results in a steady angular deflection ψ. The greater the current is, the greater the deflection is, and thus the greater the torque required of the spring is. If a current of 100 μA produces an angular deflection of 28°, what must be the torsional constant κ of the spring, as used in Eq. 15-22 (τ = -κψ )? 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-7 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-10 The Magnetic Dipole Moment 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

28-10 The Magnetic Dipole Moment U has a minimum value of –μB for (position of stable equilibrium). U has a maximum value of μB for (position of unstable equilibrium). Note: For both positions, the net torque τ=0. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-8 A circular coil with 250 turns, an area A of 2.52 × 10-4 m2, and a current of 100 μA. The coil is at rest in a uniform magnetic field of magnitude B = 0.85 T, with its magnetic dipole moment initially aligned with . (a) What is the direction of the current in the coil? (b) How much work would the torque applied by an external agent have to do on the coil to rotate it 90° from its initial orientation, so that is perpendicular to and the coil is again at rest? 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 Example 28-8 The current is from top to bottom. 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授 End of chapter 28! 2018/11/16 普通物理講義-28 / 國立彰化師範大學物理系/ 郭艷光教授