普通物理 General Physics 29 - Current-Produced Magnetic Field 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-29/國立彰化師範大學物理系/郭艷光教授 Outline 29-1 What Is Physics? 29-2 Calculating the Magnetic Field Due to a Current 29-3 Force Between Two Parallel Currents 29-4 Ampere’s Law 29-5 Solenoids and Toroids 29-6 A Current-Carrying Coil as a Magnetic Dipole 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 29-1 What Is Physics? In this chapter, we will explore the relationship between an electric current and the magnetic field it generates in the space around it. We will follow a two-prong approach, depending on the symmetry of the problem. For problems with low symmetry, we will use the law of Biot-Savart in combination with the principle of superposition. For problems with high symmetry, we will introduce Ampere’s law. 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-2 Calculating the Magnetic Field Due to a Current The law of Biot-Savart The constant A and is known as “permeability constant”. 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-2 Calculating the Magnetic Field Due to a Current Magnetic field generated by a long straight wire 2018/12/8 彰化師大教學卓越－普物教材－理學院長郭艷光主持 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 5

29-2 Calculating the Magnetic Field Due to a Current 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-2 Calculating the Magnetic Field Due to a Current Magnetic field generated by a circular wire arc of radius R at its center C . For a circular wire, 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-2 Calculating the Magnetic Field Due to a Current Magnetic field generated by a circular loop along the loop axis 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-1 The wire in Fig. 29-8a carries a current i and consists of a circular arc of radius R and central angle π/2 rad, and two straight sections whose extensions intersect the center C of the arc. What magnetic field does the current produce at C? 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-1 Solutions: 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-2 Figure 29-9a shows two long parallel wires carrying currents i1 and i2 in opposite directions. What are the magnitude and direction of the net magnetic field at point P? Assume the following values: i1 = 15 A, i2 = 32 A, and d = 5.3 cm. 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-2 Solutions: 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-2 Solutions: 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-3 Force Between Two Parallel Currents 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 29-4 Ampere’s Law The line integral of the magnetic field along any closed path is equal to the total current enclosed inside the path multiplied by μ0 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 29-4 Ampere’s Law Implementation of Ampere’s law： Magnetic field outside a long straight wire : 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 29-4 Ampere’s Law Magnetic field inside a long Straight wire R r B O 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-3 Figure 29-16a shows the cross section of a long conducting cylinder with inner radius a 2.0 cm and outer radius b = 4.0 cm. The cylinder carries a current out of the page, and the magnitude of the current density in the cross section is given by J = cr2, with c = 3.0 × 106 A/m4 and r in meters. What is the magnetic field at a point that is 3.0 cm from the central axis of the cylinder? 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-3 Solutions: 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-3 Solutions: Direction：counterclockwise 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-5 Solenoids and Toroids 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-5 Solenoids and Toroids 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-5 Solenoids and Toroids 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-4 A solenoid has length L = 1.23 m and inner diameter d = 3.55 cm, and it carries a current i = 5.57 A. It consists of five close-packed layers, each with 850 turns along length L. What is B at its center? 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 Example 29-4 Solutions: 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-6 A Current-Carrying Coil as a Magnetic Dipole The magnetic field of a magnetic dipole 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

29-6 A Current-Carrying Coil as a Magnetic Dipole The magnetic field of a magnetic dipole 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授

普通物理講義-29/國立彰化師範大學物理系/郭艷光教授 End of chapter 29! 2018/12/8 普通物理講義-29/國立彰化師範大學物理系/郭艷光教授