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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In the circuit shown in Figure 18.87, bulbs 1 and 2 are identical in mechanical construction (the filaments have the same length and the same cross-sectional area), but the filaments are made of different metals. The electron mobility in the metal used in bulb 2 is three times as large as the electron mobility in the metal used in bulb 1, but both metals have the same number of mobile electrons per cubic meter. The two bulbs are connected in series to two batteries with thick copper wires (like your connecting wires).
(a)In bulb 1, the electron current is and the electric field is . In terms of these quantities, determine the corresponding quantities and for bulb 2, and explain your reasoning.
(b)When bulb 2 is replaced by a wire, the electron current through bulb 1 is and the electric field in bulb 1 is . How big is in terms of ? Explain your answer, including explicit mention of any approximations you must make. Do not use ohms or series-resistance equations in your explanation, unless you can show in detail how these concepts follow from the microscopic analysis introduced in this chapter.
(c)Explain why the electric field inside the thick copper wires is very small. Also explain why this very small electric field is the same in all of the copper wires, if they all have the same cross-sectional area.
(d)Figure 18.88 is a graph of the magnitude of the electric field at each location around the circuit when bulb 2 is replaced by a wire. Copy this graph and add to it, on the same scale, a graph of the magnitude of the electric field at each location around the circuit when both bulbs are in the circuit. The very small field in the copper wires has been shown much larger than it really is in order to give you room to show how that small field differs in the two circuits.
The emf of a particular flashlight battery is 1.7 V. If the battery is 4.5 cm long and radius of cylindrical battery is 1 cm, estimate roughly the amount of charge on the positive end plate of the battery.
At a typical drift speed of , an electron traveling at that speed would take about to travel through one of your connecting wires. Why, then, does the bulb light immediately when the connecting wire is attached to the battery?
Since there is an electric field inside a wire in a circuit, why don’t the mobile electrons in the wire accelerate continuously?
A steady-state current flows through the Nichrome wire in the circuit shown in Figure 18.90. Before attempting to answer the following 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.
(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 some excess negative charge on the surface of the wire near location B.
(2) Inside the metal wire the magnitude of the electric field is zero.
(3) The magnitude of the electric field is the same at locations Gand C.
(4) The electric field points to the left at location G.
(5) There is no excess charge on the surface of the wire.
(6) There is excess charge on the surface of the wire near the batteries but nowhere else.
(7) The magnitude of the electric field inside the wire is larger at location Gthan at location C.
(8) The electric field at location Dpoints to the left.
(9) Because the current is not changing, the circuit is in static equilibrium.
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