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Chapter 18: Q46 P (page 761)

In the circuit shown figure 18.108, two thick copper wires connect a 1.5 V battery to a Nichrome wire. Each thick connecting wire is 17 cm long and has a radius of 9 mm. Copper has 8.4脳1028mobile electrons per cubic meter and electron mobility. The Nichrome wire is 8 cm long and has a radius of 3 mm. Nichrome has 9脳1028mobile electrons per cubic meter and electron mobility of 7脳10-5(ms)(Vm).

(a) What is the magnitude of the electric field in the thick copper wire?

(b) What is the magnitude of the electric field in the thin Nichrome wire?

Short Answer

Expert verified

The magnitude of the electric field inside copper wire is8.82V/m.

Step by step solution

01

Identification of the given data

The emf of the battery is 蔚=1.5V.

The charge density for copper wire is nc=8.4脳1028electrons/m3

The length of the copper wire is role="math" localid="1668668353251" lc=17cm

The radius of copper wire is rc=9mm

The electron mobility of copper wire is 渭c=4.4脳10-3ms/Vm

The magnitude of the electric field inside the copper wire is found by dividing the emf of the battery by the length of the copper wire.

02

Determination of magnitude of the electric field inside copper wire.

The magnitude of the electric field inside copper wire is given as:

Ec=Vlc

Substitute all the values in the above equation.

Ec=1.5V17cm1m100cmEc=8.82Vm

Therefore, the magnitude of the electric field inside copper wire is 8.82V/m.

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Most popular questions from this chapter

A Nichrome wire 30 cm long and 0.25 mm in diameter is connected to a 1.5 V flashlight battery. What is the electric field inside the wire? Why you don鈥檛 have to know how the wire is bent? How would your answer change if the wire diameter change were 0.35 mm? (Not that the electric field in the wire is quiet small compared to the electric field near a charged tape.)

Question: Three identical light bulbs are connected to two batteries as shown in Figure 18.106. (a) To start the analysis of this circuit you must write energy conservation (loop) equations. Each equation must involve a round-trip path that begins and ends at the same location. Each segment of the path should go through a wire, a bulb, or a battery (not through the air). How many valid energy conservation (loop) equations is it possible to write for this circuit? (b) Which of the following equations are valid energy conservation (loop) equations for this circuit? E1refers to the electric field in bulb 1; L refers to the length of a bulb filament. Assume that the electric field in the connecting wires is small enough to neglect.

(1) +E2L-E3L=0, (2) E1L-E3L=0, (3)+2emf-E2L-E3L=0, (4)E1L-E2L=0, (5)+2emf-E1L-E2L=0, (6)+2emf-E1L-E3L=0, (7)+2emf-E1L-E2L-E3L=0. (c) It is also necessary to write charge conservation equations (node) equations. Each such equation must relate electron current flowing into a node to electron current flowing out of a node. Which of the following are valid charge conservation equations for this circuit? (1)i1=i3, (2)i1=i2, (3)i1=i2+i3. Each battery has an emf of 1.5V. The length of the tungsten filament in each bulb is 0.008m. The radius of the filament is5脳10-6m(it is very thin!). The electron mobility of tungsten is localid="1668588909714" 1.8脳10-3(m/s)/(V/m). Tungsten has localid="1668588927161" 6脳1028mobile electrons per cubic meter. Since there are three unknown quantities, we need three equations relating these quantities. Use any two valid energy conservation equations and one valid charge conservation equation to solve for localid="1668588943223" E1,E2,i1and localid="1668588965567" i2.

Question: A circuit is constructed from two batteries and two wires, as shown in Figure 18.104. Each battery has an emf of 1.3V. Each wire is26cmlong and has a diameter of 7脳10-4m. The wires are made of a metal that has7脳1028mobile electrons per cubic meter; the electron mobility is 5脳10-5(m/s)/(V/m). A steady current runs through the circuit. The locations marked by 脳and labeled by a letter are in the interior of the wire. (a) Which of these statements about the electric field in the interior of the wires, at the locations marked by 脳's, are true? List all that apply. (1) The magnitude of the electric field at location G is larger than the magnitude of the electric field at location F. (2) At every marked location the magnitude of the electric field is the same. (3) At location B the electric field points to the left. (b) Write a correct energy conservation (round-trip potential difference) equation for this circuit, along a round-trip path starting at the negative end of battery 1 and traveling counterclockwise through the circuit (that is, traveling to the left through the battery, and continuing on around the circuit in the same direction). (c) What is the magnitude of the electric field at location B? (d) How many electrons per second enter the positive end of battery 2? (e)If the cross-sectional area of both wires were increased by a factor of 2, what would be the magnitude of the electric field at location B? (f) Which of the diagrams in Figure 18.105 best shows the approximate distribution of excess charge on the surface of the circuit?

Since there is an electric field inside a wire in a circuit, why don鈥檛 the mobile electrons in the wire accelerate continuously?

Why does the brightness of a bulb not change noticeably when you use longer copper wires to connect it to the battery? (1) Very little energy is dissipated in the thick connecting wires. (2) The electric field in connecting wires is very small, so emf鈮�EbulbLbulb. (3) Electric field in the connecting wires is zero, so emf鈮�EbulbLbulb. (4) Current in the connecting wires is smaller than current in the bulb. (5) All the current is used up in the bulb, so the connecting wires don鈥檛 matter.
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