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Chapter 18: Q6Q (page 755)
Why don’t all mobile electrons in a metal have exactly the same speed?
All mobile electrons in a wire don't have the exact same speed because the rate of collision is different for different electrons. The average speed remains constant.
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What is the most important general difference between a system in steady state and a system in equilibrium?
The circuit shown in Figure 18.107 consists of a single battery, whose emf is , and three wires made of the same material but having different cross-sectional areas. Each thick wire has a cross-sectional area and is long. The thin wire has a cross-sectional area and is long. In this metal, the electron mobility is , and there are mobile electrons/m3.
(a) Which of the following statements about the circuit in the steady state are true? (1) At location B, the electric field points toward the top of the page. (2) The magnitude of the electric field at locations F and C is the same. (3) The magnitude of the electric field at locations D and F is the same. (4) The electron current at location D is the same as the electron current at location F . (b) Write a correct energy conservation (loop) equation for this circuit, following a path that starts at the negative end of the battery and goes counterclockwise. (c) Write this circuit's correct charge conservation (node) equation. (d) Use the appropriate equation(s), plus the equation relating electron current to electric field, to solve for the magnitudes EDand EF of the electric field at locations D and F . (e) Use the appropriate equation(s) to calculate the electron current at location D in the steady state.
In the circuit shown in Figure 18.91, all of the wire is made of Nichrome, but one segment has a much smaller cross-sectional area. On a copy of this diagram, using the same scale for magnitude that you used in the previous question for Figure 18.90, show the steady-state electric field at the locations indicated, including in the thinner segment. Before attempting to answer these questions, draw a copy of this diagram. All of the locations indicated by letters are inside the wire.
(a)On your diagram, show the electric field at the locations indicated, paying attention to relative magnitude. Use the same scale for magnitude as you did in the previous question.
(b)Carefully draw pluses and minuses on your diagram to show the approximate surface charge distribution that produces the electric field you drew. Make your drawing show clearly the differences between regions of high surface charge density and regions of low surface-charge density. Use your diagram to determine which of the following statements about this circuit are true.
(1) There is a large gradient of surface charge on the wire between locations Cand E. (2) The electron current is the same at every location in this circuit.
(3) Fewer electrons per second pass location Ethan location C.
(4) The magnitude of the electric field at location Gis smaller in this circuit than it
was in the previous circuit (Figure 18.90).
(5) The magnitude of the electric field is the same at every location in this circuit.
(6) The magnitude of the electric field at location D is larger than the magnitude of the electric field at location G.
(7) There is no surface charge at all on the wire near location G.
(8) The electron current in this circuit is less than the electron current in the previous circuit (Figure 18.90).
What is the most important general difference between a system in steady state and a system in equilibrium?
Inside a chemical battery it is not actually individual electrons that are transported from the + end to the – end. At the + end of the battery an “acceptor” molecule picks up an electron entering the battery, and at the – end a different “donor” molecule gives up an electron, which leaves the battery. Ions rather than electrons move between the two ends to support the charge inside the battery.
When the supplies of acceptor and donor molecules are used up in a chemical battery, the battery is dead because it can no longer accept or electron. The electron current in electron per second times the number of seconds of battery life, is equal to the number of donor molecules in the battery.
A flashlight battery contains approximately half a mole of donor molecules. The electron current through a thick filament bulb powered by two flashlight batteries in series is about 0.3 A. About how many hours will the batteries keep this bulb lit?
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