Lesson 1.1 Electrostatics PDF

UNIT I: ELECTRICITY AND MAGNETISM IN A RELATIONSHIP CHAPTER 1 | SHOCKING! LESSON 1.1 | ELECTROSTATICS LESSON 1.2 | COULOMB’S LAW LESSON 1.3 | ELECTRIC FIELD  CHAPTER 1 | SHOCKING! BIG IDEA Charges at Rest and Electric Fields...

UNIT I: ELECTRICITY AND MAGNETISM IN A RELATIONSHIP CHAPTER 1 | SHOCKING! LESSON 1.1 | ELECTROSTATICS LESSON 1.2 | COULOMB’S LAW LESSON 1.3 | ELECTRIC FIELD  CHAPTER 1 | SHOCKING! BIG IDEA Charges at Rest and Electric Fields THEME FOCUS Electrostatic forces and the associated electric fields are governed by Coulomb’s law. LESSON 1.1 | ELECTROSTATICS MAIN IDEA Objects become electrically charged either by gaining or losing electrons. ESSENTIAL QUESTION Why do people experience electric shock? ELECTROSTATICS As early as 600 BC, the Greeks were already aware that amber—a hardened translucent yellowish tree resin— when vigorously rubbed with a piece of cloth, could attract nearby objects. THE AMBER ROOM ELECTROSTATICS In 1600, William Gilbert, who served as physician to Queen Elizabeth I of England, found out that many other substances demonstrated the same ability as that of amber when rubbed against another substance. He called these substances electrics and this ability of amber electricity, from the Greek word elektron, which means “amber.” ELECTROSTATICS Subsequently, it was shown that some objects acquire the ability to attract small pieces of matter after being rubbed against another object. The object attracted is said to have acquired a charge or become electrified. Because the charge is at rest, it is often referred to as static electricity. Electrostatics is the study of all phenomena associated with electric charges at rest. STRUCTURE OF THE ATOM To understand electrostatics, the structure of the atom must first be understood. Recall that an atom is made up of subatomic particles—protons, neutrons, and electrons. Protons and neutrons constitute the nucleus of an atom, while electrons orbit an atom’s nucleus. The mass of a proton is almost equal to the mass of a neutron. The mass of an electron is very small compared to that of a proton or a neutron. Thus, the mass of an atom is concentrated at the nucleus. In an electrically neutral atom, the number of protons is equal to the number of electrons. STRUCTURE OF THE ATOM In terms of charge, the proton is positively charged, the electron is negatively charged, and the neutron carries no charge. The charge of a proton is equal but opposite to the charge of an electron. The elementary charge (represented by e) is the electric charge carried by a single proton. It is a fundamental physics constant. Thus, a proton has a charge of +e, while an electron has a charge of –e. STRUCTURE OF THE ATOM Electrical charges are usually represented by q. The SI unit of charge is the coulomb (C), named after French physicist Charles-Augustin de Coulomb, who made important discoveries in electricity. A coulomb is approximately equal to 6.24x1018 e. Equivalently, 1e = 1.602x10-19 C. Thus, the charges of proton and electron are 1.602x10-19 C and -1.602x10-19 C, respectively. STRUCTURE OF THE ATOM PROPERTIES OF PROTON, NEUTRON, AND ELECTRON Subatomic Location Mass Charge Particle Proton inside nucleus 1.673x10-27 kg 1.602x10-19 C Neutron inside nucleus 1.675x10-27 kg 0 Electron around nucleus 9.109x10-31 kg -1.602x10-19 C CONDUCTIVITY—CONDUCTORS Charges exist in materials and move through them. However, the ease with which charges move through them differs. Conductivity is the measure of the ease at which an electric charge moves through a material. Materials that readily allow the flow of charges through them are called conductors. Metals are good conductors because they have plenty of free electrons that can easily move in the material. CONDUCTIVITY—INSULATORS Insulators are materials that resist the flow of charges. Thus, the conductivity of insulators is low. Some examples of insulators are rubber, plastic, mica, paper, glass, and air. CONDUCTIVITY—SEMICONDUCTORS Semiconductors are intermediate between conductors and insulators. Semiconductors are not as conductive as metals, but they are more conductive than insulators. The conductivity of a semiconductor in its pure form is very low. Atoms of different elements in very small amounts (i.e., one part per million or even less) are added to pure semiconductors to improve their conductivity. This process is referred to as doping.  CONDUCTIVITY—SEMICONDUCTORS Semiconductors have paved the way for the development of miniaturized electronic devices such as transistors and integrated circuits. Some examples of semiconductors are silicon, germanium, and gallium arsenide. CONDUCTIVITY—SUPERCONDUCTORS Superconductors offer practically no resistance to the flow of charges below some critical temperatures. A current in a superconductor can keep flowing without any decay. CONDUCTIVITY—SUPERCONDUCTORS In 1911, Dutch physicist Heike Kamerlingh Onnes discovered superconductivity by cooling mercury to at temperature about 4 K. Most superconductors only work at temperatures close to absolute zero. Scientists are now focused on developing superconductors that will work at normal and high temperatures. Superconductors that work at room temperature would make everyday electricity generation and transmission vastly more efficient inasmuch as there will be no power losses. PROCESS OF CHARGING In a neutral atom, the number of protons and electrons are equal. However, an atom may gain or lose electrons. If the atom gains electrons, it becomes negatively charged; if it loses electrons, it becomes positively charged. A neutral body may be charged through friction, conduction, and induction. CHARGING BY FRICTION Charging by friction results when two different materials are rubbed together. The material that will either become positively charged or negatively charged depends on its electron affinity. Electron affinity is a measure of the attraction of an atom to an electron, or the tendency of an atom to become negatively charged. CHARGING BY FRICTION Materials with higher electron affinity are capable of gaining electrons from those of lower electron affinity. Scientist have come up with a ranking of some common materials based on their electron affinity. This ranking is called the triboelectric series. In general, when two different materials are rubbed together, the one that is higher on the list will become positively charged. TRIBOELECTRIC SERIES  SAMPLE PROBLEMS 1.1 1. A rubber comb runs through human hair. What charge is acquired by the hair and by the comb? Answer: In the triboelectric series, the electron affinity of human hair is lower than that of rubber. Therefore, the hair becomes positively charged and the comb becomes negatively charged.  PRACTICE EXERCISES 1.1 1. A piece of nylon cloth is used to clean the lenses of a pair of eyeglasses. In doing so, which becomes positively charged? Which becomes negatively charged? Assume that the lenses are made of glass. Answer: lens = + nylon = -  SAMPLE PROBLEMS 1.1 2. When a glass rod is rubbed with a silk cloth, the rod acquires a charge of magnitude 3.45 nC. a) Did the glass rod gain or lose electrons? Answer: a. Because the electron affinity of glass is lower than that of silk in the triboelectric series, the glass rod loses electrons.  SAMPLE PROBLEMS 1.1 2. When a glass rod is rubbed with a silk cloth, the rod acquires a charge of magnitude 3.45 nC. b) How many electrons were transferred during the process? Answer: b. Because the glass rod becomes positively charged, the number of protons is greater than the number of electrons. To get the number of excess protons, the charge of the glass rod must be divided by the charge of the proton.  SAMPLE PROBLEMS 1.1 Answer: b. Because the glass rod becomes positively charged, the number of protons is greater than the number of electrons. To get the number of excess protons, the charge of the glass rod must be divided by the charge of the proton. 3.45×10−9 𝐶 number of excess protons = = 2.154 × 1010 1.602×10−19 𝐶 Therefore, the number of electrons gained by the silk cloth is approximately 2.154 × 1010.  SAMPLE PROBLEMS 1.1 2. When a glass rod is rubbed with a silk cloth, the rod acquires a charge of magnitude 3.45 nC. c) What is the change in the mass of the glass rod? d) What is the change in the mass of the silk cloth? Answers: c. The glass rod lost 2.154 × 1010 electrons. The mass of the glass rod decreased by an amount equal to the mass of 2.154 × 1010 electrons. The mass of an electron is 9.109 × 10−31 𝑘𝑔.  SAMPLE PROBLEMS 1.1 Answers: c. The glass rod lost 2.154 × 1010 electrons. The mass of the glass rod decreased by an amount equal to the mass of 2.154 × 1010 electrons. The mass of an electron is 9.109 × 10−31 𝑘𝑔. Thus, 10 9.109×10−31 𝑘𝑔 decrease in the mass of the glass rod = 2.154 × 10 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 ( ) 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 = 1.962 × 10−20 𝑘𝑔 d. The mass of the silk cloth is increased by 1.962 × 10−20 𝑘𝑔.  PRACTICE EXERCISES 1.1 2. In the process of rubbing the lenses of the eyeglasses, 6.28 × 1010 electrons were transferred. a) What is the charge of the lenses and the nylon cloth? b) What is the change in their masses? CHARGING BY CONDUCTION Charging by Conduction requires physical contact between a charging body and a neutral body. The sign of the charge acquired by the neutral body is the same as that of the charged body. A neutral body becomes positively charged when charged by a positively charged body. Likewise, it becomes negatively charged when charged by a negatively charged body. CHARGING BY CONDUCTION CHARGING BY CONDUCTION CHARGING BY INDUCTION A neutral body may also be charged without physical contact with a charged body. This process is called induction. In induction, the body to be charged is brought very near the charging body. The negative charges on the neutral body are attracted to the charging body if the latter is positive. They are repelled from the charging body if it is negatively charged. This effect is known as polarization. The neutral body is then grounded either by touching it or by using a wire. CHARGING BY INDUCTION Earth is a huge reservoir of charges. It can donate or accept electrons. The electrons from the neutral body will travel down the ground if the charging body is negative. The electrons will travel up the ground connection to the neutral body if the charging body is positive. The ground connection is removed followed by the charging body, leaving the previously neutral body with a net charge. This net charge is opposite to that of the charging body. CHARGING BY INDUCTION CHARGING BY INDUCTION CONSERVATION OF CHARGE Another important concept in electrostatics is the conservation of charge. The principle of conservation of charge states that the total charge of an isolated system remains constant. It means that charges can neither be created nor destroyed. In any charging process, charges are merely transferred from one body to another. CONSERVATION OF CHARGE In one of his experiments, Coulomb showed that when a sphere with an initial charge 𝒒𝟎 is brought in contact with an identically uncharged sphere, they equally share the total charge. If the spheres are not identical, they share the total according to their radii, with the quantity of charge directly proportional to their radii. The principle of conservation of charge is a universal conservation law. No experimental evidence of a violation of this law has been observed.  SAMPLE PROBLEMS 1.2 1. Metal sphere A has a net charge of +6.0 C. It is brought in contact with a neutral metal sphere B and then separated. Find the final charges on spheres A and B if (a) the spheres have equal radius and (b) if the radius of sphere B is twice the radius of sphere A.  SAMPLE PROBLEMS 1.2 2. Spheres A, B, and C have charges +8.0 C, +12.0 C, and –5.0 C, respectively. The three spheres are allowed to touch each other simultaneously and then separated. (a) What is the total charge on the three spheres before and after touching each other? (b) What is the final charge on each sphere assuming they are identical? (c) What is the final charge on each sphere assuming 𝑟𝐴 = 𝑟𝐵 = 2𝑟𝐶 ?  PRACTICE EXERCISES 1.2 1. Sphere A has an initial charge 𝒒𝟎. How many successive contacts with an uncharged identical sphere must be made to reduce the charge of sphere A to 1Τ32 of its initial charge?  PRACTICE EXERCISES 1.2 2. Spheres A, B, and C have charges +8.0 C, +12.0 C, and –5.0 C, respectively. Sphere A and B touched each other simultaneously and then separated. Sphere A then touched sphere C and then separated. (a) What is the total charge on the three spheres before and after touching each other? (b) What is the final charge on each sphere assuming they are identical? (c) What is the final charge on each sphere assuming 𝑟𝐴 = 𝑟𝐵 = 2𝑟𝐶 ?