普通物理 General Physics 22 - Finding the Electric Field－I 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-22 / 國立彰化師範大學物理系/ 郭艷光教授 Outline 22-1 What Is Physics? 22-2 The Electric Field 22-3 Electric Field Lines 22-4 The Electric Field Due to a Point Charge 22-5 The Electric Field Due to an Electric Dipole 22-6 The Electric Field Due to a Line of Charge 22-7 The Electric Field Due to a Charged Disk 22-8 A Point Charge in an Electric Field 22-9 A Dipole in an Electric Field 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 22-1 What Is Physics? As long as charges are stationary, Coulomb’s law described adequately the forces among charges. If the charges are not stationary, we must use an alternative approach by introducing the electric field. (symbol ) charge q1 →generates electric field → exerts a force in q2 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 22-2 The Electric Field 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 22-3 Electric Field Lines At any point P, the electric field vector is tangent to the electric field lines. The magnitude of the electric field vector is proportional to the density of the electric field lines. P Electric field line Electric field lines P Q 3. Electric field lines extend away from positive charges (where they originate) and towards negative charges (where they terminate). 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 22-3 Electric Field Lines 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 22-3 Electric Field Lines The electric field on either side of the plane has a constant magnitude. The electric field vector is perpendicular to the plane. The electric field vector points away from the plane. 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-4 The Electric Field Due to a Point Charge q qo r P 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-4 The Electric Field Due to a Point Charge 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-1 Three particles with charges q1 = 2Q, q2 = 2Q, and q3 = 4Q, each a distance d from the origin. What net electric field is produced at the origin? 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-1 Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-5 The Electric Field Due to an Electric Dipole 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-2 Sprites are not well understood but are believed to be produced when especially powerful lightning occurs between the ground and storm clouds, particularly when the lightning transfers a huge amount of negative charge -q from the ground to the base of the clouds. 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-2 Just after such a transfer, the ground has a complicated distribution of positive charge. However, we can model the electric field due to the charges in the clouds and the ground by assuming a vertical electric dipole that has charge -q at cloud height h and charge +q at below-ground depth h. If q = 200 C and h = 6.0 km, what is the magnitude of the dipole’s electric field at altitude z1 = 30 km somewhat above the clouds and altitude z2 = 60 km somewhat above the stratosphere? 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-2 Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-6 The Electric Field Due to a Line of Charge dq 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-3 A plastic rod having a uniformly distributed charge -Q. The rod has been bent in a 120° circular arc of radius r. We place coordinate axes such that the axis of symmetry of the rod lies along the x axis and the origin is at the center of curvature P of the rod. In terms of Q and r, what is the electric field due to the rod at point P? 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-3 Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-3 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-7 The Electric Field Due to a Charged Disk 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-8 A Point Charge in an Electric Field 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-4 The deflecting plates of an ink-jet printer, with superimposed coordinate axes. An ink drop with a mass m of 1.3 × 10-10 kg and a negative charge of magnitude Q = 1.5 × 10-13 C enters the region between the plates, initially moving along the x axis with speed vx = 18 m/s. 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-4 The length L of each plate is 1.6 cm. The plates are charged and thus produce an electric field at all points between them. Assume that field is downward directed, is uniform, and has a magnitude of 1.4 × 106 N/C. What is the vertical deflection of the drop at the far edge of the plates? (The gravitational force on the drop is small relative to the electrostatic force acting on the drop and can be neglected.) 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-4 Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-9 A Dipole in an Electric Field -q +q/2 F+ F- x-axis 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-9 A Dipole in an Electric Field Potential energy of an electric dipole in a uniform electric field A B  U 180˚ 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

22-9 A Dipole in an Electric Field 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-5(a) A neutral water molecule (H2O) in its vapor state has an electric dipole moment of magnitude 6.2 × 1030 C ·m. How far apart are the molecule’s centers of positive and negative charge? 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-5(a) Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-5(b) If the molecule is placed in an electric field of 1.5 × 104N/C, what maximum torque can the field exert on it? (Such a field can easily be set up in the laboratory.) 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-5(b) Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-5(c) How much work must an external agent do to rotate this molecule by 180 in this field, starting from its fully aligned position, for which θ = 0? 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 Example 22-5(c) Solutions: 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授 End of chapter 22! 2019/1/17 普通物理講義-22 / 國立彰化師範大學物理系/ 郭艷光教授