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講者: 許永昌 老師 1 Contents Electric Field created by charge : Discrete continuous Idea: . Picturing the electric field by Discrete: Continuous: Problem solving strategy Important Examples: , . , , , and . Motion of charged particles in the field: Uniform Electric Field: Parallel-Plate Capacitor Non-uniform Electric Field 2 Electric Field created by charge (請預 讀P818~P821) Electric field created by a E : 1 q rˆ. 2 4 0 r Electric field created by a group of charges: Fon q ' F1 on q ' F2 on q ' ..., Enet Fon q ' F1 on q ' F2 on q ' ... E1 E2 ... q' q' q' 這兩條方程是本章所有計算的出發點。 3 Limiting Case Electric Field is A function of , Related to the . Limiting Case: Very far or very close to an charged object. Change the size of the charged object to be infinitely small or large. Etc. 1 Qnet Example: The electric field at r is E rˆ. 2 4 0 r 4 Exercise Try to use the Problem-Solving Strategy (P820) to find the electric field of three equal point charges on the x+ axis. d d + + Ex=? Limiting Case? x0 and x>>0. 5 Electric Field of a Dipole (請預讀 P822~P823) Electric_field_of_a_dipole.m There are two kinds of electric dipoles: Permanent electric dipole: H2O, … Induced electric dipole: O2,… 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 1.5 2kp E 3 r 1 0.5 0 -0.5 -1 -1.5 -1.5 -1 -0.5 0 0.5 1 2 1.5 + s - E : Prove it. kp r3 qs, from the negative p to the positive charge Dipole moment p. 6 Picturing the Electric Field (請預讀 P824) Electric Field lines is one kind of representation of electric field. The concept is the similar to the and we discussed in P460, Ch15. Will be discussed in Ch18. 7 Electric Field lines It tell you the exact magnitude of electric field. It is a good conceptual tool. 8 Homework Student Workbook: 2, 4, 7, 11, 12 9 Electric Field of a Continuous Charge Distribution (請預讀P825~P828) We need the concept of Q Linear Charge density: l lim . L 0 : L Q h lim . Surface Charge density: A 0 A DQ=hDA. Q Volume Charge density:r lim . V 0 V DQ=rDV. DQ=lDL. Q, #1 a b #2 #3 : The surface charge density of object 1? The original one broken into the smaller ones. Compare the surface charge densities h1, h2 and h3. 10 Problem solving Strategy(請預讀P826) : For the pictorial representation. Draw a picture and establish a system. Divide the total charge Q into . Draw the electric field vector at desired point for of charge. (純粹為了方便找到必要的參數) This will help you that need to be calculated. Look for of the charge distribution that simplify the field. : Use the concept of superposition to find the Translate the sum into an from a sum. (dQ=ldx). Q: How to do the integration for a vector field? 此處困難點常常是在於不曉得怎麼寫出相應的積分。 11 Homework Student Workbook: 15, 16, 18, 19, 20 12 Electric Field of Lines (請預讀P827~P828) Visualize 1. 1. 2. 3. Known Coordinate (considered with symmetry) Length Charge Separate the object into small pieces Plot some electric fields on the desired point. L Q 2. Solving x 1. Ei x Ei cos Ei 2. 3. Enet yi2 x 2 N N i 1 i 1 xˆ Ei x xˆ N Enet xˆ i 1 xˆ k lDyi y 2 i x2 2 yi2 x2 yi2 x 2 kQ x x2 L k DQi x 2 . , L 2 L 2 xˆ y x yi2 x 2 kxl 2 x2 3 . dy 2 + + + + + + + + x 13 Limit case of a line Electric field on the x axis: Enet xˆ kQ 2 x x2 L If x>>L, 2 . kQ xˆ . It behaves as a charge Q. Reasonable. x2 2kQ 2k l xˆ xˆ . Enet l and 1/x. xL x Enet If x<<L, Enet 14 Exercise Please find the electric field at point p. l p L r 15 The electric field of a ring and a disk(請預讀P829~P832) Visualize 1. 1. 2. 3. Coordinate (considered with symmetry) Separate the object into small pieces Plot some electric fields on the desired point. 2. Solving 線和面的計算原理相同 都用到superposition. Ring: E kzQ . z z2 r2 z 3/ 2 r Disk: E N z i 1 kzDQi z ri 2 2 3/ 2 DQi h 2 ri Dri R 0 Dr kzh 2 rdr z2 r2 3/ 2 h z z 2 2 0 z z R2 . 16 Limiting case of a disk Electric field of a disk, z>0 part: E z h 1 2 0 z>> R (far enough), E z h 1 1 2 2 0 1 R / z h R2 Q . 2 2 4 0 z 4 0 z . 2 2 z R z 2 h 1 1 1 R 2 0 2 z 2 (當第一階近似為零,就要再找下一階) 0<z<<R (close enough), E z h h z z h 1 . 1 2 2 2 0 2 R 2 z R 0 0 It is a constant! 17 The electric field of a uniform charged sphere (請預讀P833) This problem is analogous to wanting to know the gravitational field of a spherical planet or star. We will discuss it in Ch28 in detail. Esphere, outside kQ rˆ. r R r2 18 The Parallel-Plate Capacitor (請預讀 P834) Therefore, we create an . + + + + + + E h 2 0 E : Can we that the right plate the electric field to the right of the capacitor? + + + + + + h 0 19 Homework Student Workbook: 22, 25, 27, 28 20 Motion of a charged particle in an Electric Field (請預讀P835~P840) We said that some charges, the , create an electric field. then to that electric field. Now we turn our attention to the second half of the interaction. The force exerted by a electric field on a charge q particle is Fon q qE. + 21 Exercises a capacitor. Sketch the particle’s trajectory if the particle’s initial velocity is (a) zero, (b) straight down, and (c) to the right. + + + + + + + How about a negatively charged particle? - A positively charged particle is in the center of A charged particle is doing the uniform circular motion around a uniform charged infinite long line. Please find its velocity. Hint: + r q/m l free-body diagram Fnet Newton’s 2nd Law a Trajectory. 22 Motion of a dipole in an Electric field (請預讀P839~P840) Dipoles in a Uniform Field: Net force: Fnet=0. p E. Torque: Dipoles in a Nonuniform Field: Net force: Fnet0. A dipole will experience a net force toward any charged object 23 Homework Student Workbook: 29, 30, 32, 34, 35, 36 Student Textbook: 47, 53 自行製造 Terms and Notation 的卡片 24