# physics 2b for materials and structural engineering ben gurion university of the negev...

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Physics 2B for Materials and Structural Engineering Ben Gurion University of the Negev www.bgu.ac.il/atomchip Lecturer: Daniel Rohrlich Teaching Assistants: Oren Rosenblatt, Irina Segel Week 1. Charge, E and Coulombs law Introduction electrical charges, quantization and conservation Coulombs law addition of electric forces electric field Sources: Halliday, Resnick and Krane, 4 th Edition, Chap. 27; Halliday, Resnick and Krane, 5 th Edition, Chaps. 25-26; Purcell (Berkeley course 2), Chap. 1, Sects. 1.3 1.4 and 1.7. Slide 2 Introduction Both electricity and magnetism were known to the ancient Greeks 2600 years ago. When they rubbed a piece of amber with fur, the amber would attract straw and hair. Slide 3 Introduction Both electricity and magnetism were known to the ancient Greeks 2600 years ago. When they rubbed a piece of amber with fur, the amber would attract straw and hair. Amber is resin that became a fossil. Slide 4 Introduction Both electricity and magnetism were known to the ancient Greeks 2600 years ago. When they rubbed a piece of amber with fur, the amber would attract straw and hair. = = = amber Slide 5 Introduction Both electricity and magnetism were known to the ancient Greeks 2600 years ago. When they rubbed a piece of amber with fur, the amber would attract straw and hair. = = = amber (,): . = amber. According to the Septuagint, Slide 6 Introduction The ancient Greeks also knew of stones that would attract iron. Magnetite from Utah, U.S.A. R.Weller/Cochise College.R.Weller/Cochise College Slide 7 2600 years ago, and even 300 years ago, electric and magnetic phenomena appeared to be very unusual. They appeared to have very little to do with the rest of nature, and nothing to do with each other. Slide 8 Today, our view is about as different from this ancient view as possible: everything in the natural world, including all of biology and chemistry, depends on electricity and magnetism; also electricity and magnetism depend on each other. Slide 9 2600 years ago, and even 300 years ago, electric and magnetic phenomena appeared to be very unusual. They appeared to have very little to do with the rest of nature, and nothing to do with each other. Today, our view is about as different from this ancient view as possible: everything in the natural world, including all of biology and chemistry, depends on electricity and magnetism; also electricity and magnetism depend on each other. Why did it take so long to see that electricity and magnetism are everywhere? Slide 10 Electrical charges, quantization and conservation Electrostatics: the study of electric charges at rest. Slide 11 Electrical charges, quantization and conservation Electrostatics: the study of electric charges at rest. How do we know that there are two kinds of charge? (We call them positive and negative, but any other names would be as good.) Slide 12 Electrical charges, quantization and conservation Electrostatics: the study of electric charges at rest. How do we know that there are two kinds of charge? (We call them positive and negative, but any other names would be as good.) Since electric charges can repel as well as attract, there must be at least two kinds. Slide 13 Electrical charges, quantization and conservation Electrostatics: the study of electric charges at rest. How do we know that there are two kinds of charge? (We call them positive and negative, but any other names would be as good.) Since electric charges can repel as well as attract, there must be at least two kinds. We have heard that same charges repel, opposite charges attract, but could it be the other way around? Could our world be a world in which opposite charges repel, same charges attract? Slide 14 Electrical charges, quantization and conservation Electric charge is quantized, and nobody knows why! Not even quantum mechanics explains (so far) why charge is quantized. All electrons have exactly the same charge e: e = (1.602 176 487 0.000 000 040) 10 -19 C Our unit of charge is C and is called a Coulomb. Slide 15 Electrical charges, quantization and conservation Electric charge is quantized, and nobody knows why! Not even quantum mechanics explains (so far) why charge is quantized. All electrons have exactly the same charge e: e = (1.602 176 487 0.000 000 040) 10 -19 C The first person to measure e was R. A. Millikan (around 1910). Slide 16 Electrical charges, quantization and conservation Electric charge is quantized, and nobody knows why! Not even quantum mechanics explains (so far) why charge is quantized. All electrons have exactly the same charge e: e = (1.602 176 487 0.000 000 040) 10 -19 C The first person to measure e was R. A. Millikan. He sprayed droplets of oil and measured the mass m of each droplet from its fall. Then he applied an electric field of strength E to balance the droplet in mid-air, and extracted e from mg = eE. Slide 17 Electrical charges, quantization and conservation The proton and the electron are very different, but the electron charge and the proton charge are known to be the same (except for sign) to an accuracy of one part in 10 20. So why did it take so long to see that electricity and magnetism are everywhere? Slide 18 Electrical charges, quantization and conservation Conservation of electric charge: The total electric charge in an isolated system does not change. There are processes that change the number of charged particles in an isolated system, but no process changes the total electric charge. Slide 19 Coulombs law Consider two fixed point charges. One is located at r 1 and has charge q 1 ; the other is located at r 2 and has charge q 2. The force of the charge located at r 1 on the charge at r 2 has magnitude where r 12 = | r 1 r 2 | and the constant k in the units of this course is q1q1 q2q2 Slide 20 Coulombs law (vector formulation) Consider two fixed point charges. One is located at r 1 and has charge q 1 ; the other is located at r 2 and has charge q 2. The force of the charge located at r 1 on the charge at r 2 is where is a unit vector pointing from r 1 to r 2. By Newton s Third Law, the force F 21 of the charge located at r 2 on the charge at r 1 is equal in magnitude and opposite in sign. q1q1 q2q2 F 21 F 12 Slide 21 Coulombs law (vector formulation) Consider two fixed point charges. One is located at r 1 and has charge q 1 ; the other is located at r 2 and has charge q 2. The force of the charge located at r 1 on the charge at r 2 is writing it a slightly different way. By Newton s Third Law, the force F 21 of the charge located at r 2 on the charge at r 1 is equal in magnitude and opposite in sign. q1q1 q2q2 F 21 F 12 Slide 22 Addition of electric forces Electric forces add like vectors! Suppose we have three fixed point charges. One is located at r 1 and has charge q 1 ; the second is located at r 2 and has charge q 2 ; the third is located at r 3 and has charge q 3. What is the total force of the charges at r 1 and r 2 on the point charge located at r 3 ? q1q1 q2q2 q3q3 Slide 23 Addition of electric forces Electric forces add like vectors! Suppose we have three fixed point charges. One is located at r 1 and has charge q 1 ; the second is located at r 2 and has charge q 2 ; the third is located at r 3 and has charge q 3. What is the total force of the charges at r 1 and r 2 on the point charge located at r 3 ? q1q1 q2q2 q3q3 F 13 F 23 Slide 24 Addition of electric forces Electric forces add like vectors! Suppose we have three fixed point charges. One is located at r 1 and has charge q 1 ; the second is located at r 2 and has charge q 2 ; the third is located at r 3 and has charge q 3. What is the total force of the charges at r 1 and r 2 on the point charge located at r 3 ? It is q1q1 q2q2 F 13 F 23 q3q3 Slide 25 Addition of electric forces Electric forces add like vectors! Suppose we have three fixed point charges. One is located at r 1 and has charge q 1 ; the second is located at r 2 and has charge q 2 ; the third is located at r 3 and has charge q 3. What is the total force of the charges at r 1 and r 2 on the point charge located at r 3 ? It is q1q1 q2q2 F 13 F 23 F 13 + F 23 q3q3 Slide 26 Addition of electric forces Example 1 (electric dipole): Two equal and opposite point charges lie on the z-axis: charge e is at z = a and charge e is at z = a. What is the force F q on a point charge q on the z-axis at arbitrary z? ee q 0 e Slide 27 Addition of electric forces Example 1 (electric dipole): Two equal and opposite point charges lie on the z-axis: charge e is at z = a and charge e is at z = a. What is the force F q on a point charge q on the z-axis at arbitrary z? Answer: ee q 0 e Slide 28 Addition of electric forces Example 1 (electric dipole): Two equal and opposite point charges lie on the z-axis: charge e is at z = a and charge e is at z = a. What is the force F q on a point charge q on the z-axis at arbitrary z? Answer: ee q 0 e Slide 29 Addition of electric forces Example 1 (electric dipole): Two equal and opposite point charges lie on the z-axis: charge e is at z = a and charge e is at z = a. What is the force F q on a point charge q on the z-axis at arbitrary z? Answer: ee q 0 for z >> a. e Slide 30 Addition of electric forces Lets continue this example with the charge q on the x-axis at arbitrary x. What is the force F q on the charge q? ee q 0 e Slide 31 Addition of electric forces Lets continue this example with the charge q on the x-axis at arbitrary x. What is the force F q on the charge q? e ee 0 q Answer: Each charge on the z-axis produces a force of magnitude F = eq/4 0 (x 2 + a 2 ) but the x-components of these forces cancel. The net force is down: Slide 32 Addition of electric forces Example 2: An infinite, stationary straight line carries uniform charge per unit length . Off the wire, a distance L from it (closest approach) is a fixed point charge of magnitude q. What is the force of the lin