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9. A pith-ball electroscope may be in a charged or a neutral state. Describe the steps you would take to determine whether it is charged or neutral. If the electroscope is charged, how would you determine what charge it possesses? Making Connections electric field: the space around a charged object where forces of attraction or repulsion act on other objects 10. While metal car bodies are being spray-painted at the factory, they are grounded. Explain the advantages of this. (Hint: As the spray leaves the nozzle at high speeds, it becomes charged.) 11. When clothes made of different materials tumble in a warm clothes dryer they have a tendency to cling to one another. Coated strips or spray may be purchased to prevent or remove the “static cling.” Research how “anti-static cling” formulations work. Follow the links for Nelson Physics 11, 12.1. GO TO www.science.nelson.com 12. Electrostatic printing, commonly known as xerography or photocopying, uses the principles of static electricity to print on paper or other materials. Research and explain the steps in the process where static electricity plays a role. Follow the links for Nelson Physics 11, 12.1. + GO TO www.science.nelson.com Reflecting 13. Would you feel comfortable working in a high-tech clean room knowing that you would have to be extremely careful about static charge? List some advantages and disadvantages of such a job. Figure 1 Electric field around a single positive charge 12.2 (a) + + Electric Fields and Electric Charge What causes electric force? How is electric charge measured? The study of charges will be far more productive if we address these questions. Electric Fields (b) – + Figure 2 Some typical electric fields. Notice that these field lines are directed away from the positive spheres and toward the negative spheres. (a) Like charges (b) Opposite charges 432 Chapter 12 Electric charges exert forces that can attract and repel each other even when they are not in direct contact. What causes the force? We don’t see anything between the charges that could be responsible for it. Yet this kind of force is already familiar to you. The force of gravity was explained in terms of a gravitational field of force—when a mass is placed in the gravitational field of another mass, the first mass experiences a force of attraction toward the second mass. It is reasonable to assume that the forces between charged objects may also be due to a field of force. If this is true, then every charged object creates an electric field of force in the space around it (Figure 1) and any other charged object in that field will experience a force of electrical attraction or repulsion. The electric field is represented by drawing a series of field lines around the charged object. Field lines show the direction of the electric force on a small positive test charge placed at each and every point in the field. It is customary to use a positive charge as a test charge. The relative distance between adjacent field lines at a given point is an indication of the strength of the electric field at that point. Some typical electric fields are shown in Figure 2. 12.2 Measuring Electric Charge A quantitative analysis of the factors affecting electric force was first performed by the French physicist Charles Augustin de Coulomb (1736–1806). By performing experiments similar to that shown in Figure 3, Coulomb found that the magnitude of the force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This famous relationship, called Coulomb’s law, was of immense importance to our understanding of electric forces. In his honour, the unit of electric charge is called the coulomb (C). To give you an idea of the magnitude of a coulomb: 1 C of electric charge is approximately the amount that would pass through a 100 W light bulb in 1 s, operating at 100 V. The relationship discovered by Coulomb can be written as: fine support wire A –– repulsion –– light horizontal bar B Coulomb’s Law kQ Q2 F = 1 d2 where k is a constant Early in the 20th century Robert A. Millikan (1868–1953), an American physicist, performed a series of experiments proving the existence of a smallest unit of electric charge; all other electric charges are simple multiples of this smallest charge. He reasoned that this elementary charge (e) is the charge on a single electron. Oil drops were sprayed into the space between two parallel metal plates (Figure 4). A light was shone on the oil drops, and they were observed through a telescope. A power supply was connected to the plates so that an electric force would act on the oil drops between the plates. An upward electric force was exerted on those drops whose charge was the same sign as the lower plate’s. By adjusting the amount of charge on the plates, it was possible to isolate a single oil drop and balance it so that the downward gravitational force and the upward electrical force were equal. Using measurements related to the “balancing field,” and the speed with which the oil drops fell when the field was removed, Millikan was able to calculate the amount of electric charge on the oil drop, in coulombs. Figure 3 Coulomb devised an experiment to measure the force of repulsion between two charged objects, with one object suspended from a bar by a vertical wire. When charged object B was brought close to charged object A, it repelled A and caused the wire to twist a measurable amount. Coulomb’s law: the magnitude of the force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them coulomb: (C) the SI unit of electric charge atomizer electrical force metal plate light source – + – charged oil drop metal plate battery calibrated telescope gravitational force Figure 4 Millikan assumed that when tiny oil drops are sprayed from an atomizer, they become charged by friction—some acquiring an excess of a few electrons, while others have a deficit. Although there was no way of knowing how many extra electrons there were on an oil drop, or how many were missing, Millikan was able to devise a technique for measuring the total amount of charge on each individual drop. Electricity 433 By repeating this procedure many times, using the same oil drop with different amounts of charge on it, and using different oil drops, Millikan was able to compile a long list of values for the amount of charge on an oil drop. But how was he able to determine the value of the charge on an electron from this list of values for the total charge on a drop? Lab Exercise 12.2.1 Investigating Data from Millikan’s Oil Drop Experiment By 1909, Robert Millikan (Figure 5) was able to determine the charge on an electron by studying the behaviour of charged oil drops. Using an apparatus where charged drops of oil fell in the presence of a strong electric field, he was able to determine that the charge on an electron was a fundamental constant of electricity. In this lab exercise, you will analyze experimental evidence obtained from Millikan’s oil drop experiment and search for patterns that yield the fundamental charge on an electron. Observations Note: The values listed below represent the charges calculated on 12 oil drops, a very small portion of the data collected by Millikan. Figure 5 Robert A. Millikan (1868–1953) was awarded the Nobel Prize for Physics in 1923. 3.2 10–19 C = 1.6 10–19 C _____________ 16.0 10–19 C = 1.6 10–19 C _____________ 17.6 10–19 C = 1.6 10–19 C _____________ 6.4 10–19 C = 1.6 10–19 C _____________ 8.0 10–19 C = 1.6 10–19 C _____________ 12.8 10–19 C = 1.6 10–19 C _____________ 11.2 10–19 C = 1.6 10–19 C _____________ 4.8 10–19 C = 1.6 10–19 C _____________ 1.6 10–19 C = 1.6 10–19 C _____________ 9.6 10–19 C = 1.6 10–19 C _____________ 19.2 10–19 C = 1.6 10–19 C _____________ 14.4 10–19 C = 1.6 10–19 C _____________ Analysis DID YOU KNOW ? Nobel Prizes for physics, chemistry, and other fields have been awarded almost annually since 1901, according to the terms of the will of Alfred Bernard Nobel (1833–96), the Swedish industrialist who invented dynamite. The awards are made by the Swedish Royal Academy of Sciences. Each prize has a cash value, which increases from year to year. (a) Copy the observations into your notebook. See if you can spot the patterns that Millikan did. (Use a calculator if necessary.) (b) List all the patterns you can find. In your own words, try to describe what these patterns might mean. Two observations were evident to Millikan when he analyzed his oil drop data: 1. The smallest value for the charge on an oil drop is 1.6 × 10–19 C. 2. All the other values are whole-numbered multiples of 1.6 × 10–19 C. Millikan called the smallest unit of charge, which is the absolute value of the charge on an electron, the elementary charge (e). The elementary charge (e) has magnitude e = 1.60 × 10–19 C 434 Chapter 12 12.2 Since an electron is a negative elementary charge and a proton is a positive elementary charge, we can conclude that the charge on one electron is –e = –1.6 × 10–19 C, and the charge on one proton is e = 1.6 × 10–19 C. 1 Also, if the elementary charge is 1.60 × 10–19 C, then it must take 1.60 × 10–19 18 or 6.24 × 10 electrons to make up 1 C of charge. For the present, we will use this as the value of a coulomb: 1 C = 6.24 × 1018 e. Using this value for the elementary charge, we can devise an equation to make an important calculation. If a charged object has an excess or deficit of N electrons, each with a charge e (the elementary charge), then the total charge, Q, on the object, measured in coulombs, is given by Q = Ne Sample Problem How many electrons have been removed from a positively charged pith-ball electroscope if it has a charge of 7.5 × 10–11 C? Solution Q = 7.5 × 10–11 C e = 1.6 × 10–19 C N=? Q N = e 7.5 × 10–11 C = 1.6 × 10–9 C N = 4.7 × 108 electrons The number of electrons removed was 4.7 × 108 electrons. Practice Understanding Concepts 1. What is the charge in coulombs on an object that has (a) an excess of 6.25 × 1019 electrons? (b) a deficiency of 1.0 × 108 electrons? 2. A polyethylene strip has a charge of –5.2 × 10–7 C. What is the excess number of electrons on the strip? SUMMARY Answers 1. (a) –1.0 × 101 C (b) +1.6 × 10–11 C 2. 3.3 × 1012 Electric Fields and Electric Charge • Every charged object creates an electric field of force in the space around it; any other charged object in that field will experience a force of electrical attraction or repulsion. • Electric charge is measured in units called coulombs (C). • Millikan’s oil drop experiment proved the existence of a smallest unit of electric charge, which he called the elementary charge (e). • The total charge, Q, on an object, measured in coulombs, is given by the equation Q = Ne. Electricity 435 Section 12.2 Questions Understanding Concepts 1. Assuming the object marked with a P in Figure 6 is positively charged and the lines represent the electric field, determine the signs of the charges on the other objects and place arrows on the lines in the correct directions. P 2. In a lightning bolt, it is estimated that a charge of 22.0 C is transferred from a cloud to Earth. How many electrons make up the lightning bolt? 3. A metal-leaf electroscope is given a negative charge of 1.2 µC by induction and grounding. How many electrons move through your finger when you touch the knob of the electroscope? Figure 6 4. An ebonite rod with an excess of 6.4 108 electrons shares its charge equally with a pith ball when they touch. What is the charge on the pith ball, in coulombs? 5. In Millikan’s experiment, oil drops that have similar charges to that on the bottom plate can become balanced so that they will float. Draw a free-body diagram of the oil drop and explain why this must be so. 6. Draw a straight horizontal line about 5 cm long in your notebook to represent a positively charged wire. Draw the electric field lines above and below the wire. (Hint: The direction of the electric field line is determined by the direction of the force experienced by a small positive test charge near the wire.) 7. Draw two straight horizontal lines about 5 cm long and parallel to each other, separated by about 2 cm. If the top line represents a positively charged plate and the bottom one a negatively charged plate, draw the electric field between the plates. Applying Inquiry Skills 8. After completing an experiment similar to Millikan’s, a student claims that the charge on the oil drop is 3.8 10–19 C. Is the measurement reasonable or is it suspect? Explain your reasoning. DID YOU KNOW ? Electric Fields in the Ocean Sharks are sensitive to the small electric field surrounding possible prey, such as fish. Experiments have shown that a shark will attack an artificial electric field and ignore a piece of food. Artificial electric fields were used at the 2000 Olympics in Australia to keep sharks away from triathalon competitors swimming in Sydney harbour. 9. Discuss how the mass of an individual marble could be calculated given several bags containing different numbers of identical marbles. You would not be allowed to see into the bag or handle it in any way. Assume the bags have very small masses and that an electronic balance is available. If the materials are available, try your method to see if it works. 10. Many people believe that electric fields can be used to treat human diseases. There are claims that exposure to low frequency electric fields is effective in treating conditions such as osteoporosis, arthritis, muscle pain, cancer, and AIDS. Research these controversial claims and determine whether they are credible. Follow the links for Nelson Physics 11, 12.2. GO TO www.science.nelson.com Reflecting 11. When Millikan was performing his famous oil drop experiment he was unaware that there existed a smallest electric charge. Initially he might have been discouraged since the measurements of the charge on the oil drop seemed to vary with no discernible pattern. What kinds of characteristics must a scientist (like Millikan) have to make such a discovery? Do you think you possess these characteristics? 436 Chapter 12