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Chapter 2: 50P-d (page 45)

Question: The following questions refer to the circuit shown in Figure 18.114, consisting of two flashlight batteries and two Nichrome wires of different lengths and different thicknesses as shown (corresponding roughly to your own thick and thin Nichrome wires).

The thin wire is 50 cm long, and its diameter is 0.25 mm. The thick wire is 15 cm long, and its diameter is 0.35 mm. (a) The emf of each flashlight battery is 1.5 V. Determine the steady-state electric field inside each Nichrome wire. Remember that in the steady state you must satisfy both the current node rule and energy conservation. These two principles give you two equations for the two unknown fields. (b) The electron mobility

in room-temperature Nichrome is about 7脳10-5(ms)(Ns). Show that it takes an electron 36 min to drift through the two Nichrome wires from location B to location A. (c) On the other hand, about how long did it take to establish the steady state when the circuit was first assembled? Give a very approximate numerical answer, not a precise one. (d) There are about 9脳1028mobile electrons per cubic meter in Nichrome. How many electrons cross the junction between the two wires every second?

Short Answer

Expert verified

The number of electrons crossing the junction is 1.72脳1018electronss.

Step by step solution

01

Write the given data

The thin wire is 50 cm long and the diameter is 0.25 mm.

The flashlight battery is1.5 V.

02

Determine the formula

Consider the equation for the current in the wire is derived as:

i=nAuE

03

Determine the number of electrons that cross the junction as:

Solve for the number of electrons that are crossing the junction as:

i=nAv=9脳1028electronsm30.04908脳1063.9脳104ms=1.72脳1028electronss

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Most popular questions from this chapter

A playground ride consists of a disk of mass M=43kgand radius R=1.7mmounted on a low-friction axle (Figure 11.94). A child of mass m=25kgruns at speed v=2.3m/son a line tangential to the disk and jumps onto the outer edge of the disk.

(a.) If the disk was initially at rest, now how fast is it rotating? (b) What is the change in the kinetic energy of the child plus the disk? (c) where has most of this kinetic energy gone? (d) Calculate the change in linear momentum of the system consisting of the child plus the disk (but not including the axle), from just before to just after impact. What caused this change in the linear momentum? (e) The child on the disk walks inward on the disk and ends up standing at a new location a distance from the axle. Now what is the angular speed? (f) What is the change in the kinetic energy of the child plus the disk, from the beginning to the end of the walk on the disk? (g) What was the source of this increased kinetic energy?

A paddle ball toy consists of a flat wooden paddle and asmall rubber ball that are attached to each other by an elastic band (Figure 2.61). You have a paddle ball toy for which the mass of the ball is 0.015 kg, the stiffness of the elastic band is 0.9 N/m, and the relaxed length of the elastic band is 0.30 m. You are holding the paddle so the ball hangs suspended under it, when your cat comes along and bats the ball around, setting it in motion. At a particular instant the momentum of the ball is鉄�-0.02,-0.01,-0.02鉄�kg鈰�m/s , and the moving ball is at location 鉄�-0.2,-0.61,0鉄�m relative to an origin located at the point where the elastic band is attached to the paddle.

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(鉄�-0.2,-0.61,0鉄�m)and momentum(鉄�-0.02,-0.01,-0.02鉄�kg鈰�m/s) , determine the position of the ball 0.1 s later, using a of 0.05 s. (c) If your answers are different, explain why.

As shown in Figure 19.74, a spherical metal shell of radius r1has a charge Q(on its surface) and is surrounded by a concentric spherical metal shell of radius r2which has a charge -Q(on its inner surface).

(a) Use the definition of capacitance: Q=C|鈻�V|to find the capacitance of this spherical capacitor.

(b) If the radii of the spherical shells r1and r2are large and nearly equal to each other, show that Ccan be written as 蔚0As(which is also the equation for the capacitance of a parallel-plate capacitor) where A=4蟺谤2is the surface area of one of the spheres, and sis the small gap distance between them r2=r1+s.

A space station has the form of a hoop of radius R=14m, with mass M=6250 kg(Figure 11.91). Initially its center of mass is not moving, but it is spinning with angular speed 蝇0=0.0013rad/sThen a small package of mass m=6kgis thrown by a spring-loaded gun toward a nearby spacecraft as shown; the package has a speedv=40m/s after launch. Calculate the center-of-mass velocity of the space station and its rational speed after the launch.

Question: the Hall effect can be used to determine the sign of the mobile charges in a particular conducting material. A bar of a new kind of conducting material is connected to a battery as shown in Figure 20.85. In this diagram, the x-axis runs to the right, the y-axis runs up, and the z-axis runs out of the page, toward you. A voltmeter is connected across the bar as shown, with the leads placed directly opposite each other along a vertical line. In order to answer the following question, you should draw a careful diagram of the situation, including all relevant charges, electric fields, magnetic fields, and velocities.

Initially, there is no magnitude filed in the region of the bar. (a) Inside the bar, what is the direction of the electric field E鈫�due to the charges on the batteries and the surface of the wires and the bar? This is the electric field that drives the current in the bar. (b) If the mobile charges in the bar are positive in what direction do they move when the current runs? (c) If the mobile charges in the bar are negative, in what direction do they move when the current runs? (d) In this situation (zero magnetic fields), what is the sign of the reading on the voltmeter?

Next, large coils (not shown) are moved near the bar. And current runs through the coils, making a magnetic field in the -z direction (into the page). (e) If the mobile charges in the bar are negative, what is the direction of the magnetic force on the mobile charge? (f) If the mobile charges in the bar are negative, which of the following things will happen? (1) Positive charge will accumulate on the top of the bar. (2) The bar will not becomes polarized. (3) Negative charge will accumulate on the left end of the bar. (4) Negative charge will accumulate on the top of the bar. (g) If the mobile charges in the bar are positive, what is the direction of the magnetic force on the mobile charges? (h) If the mobile charges in the bar are positive, which of these things will happen? (1) positive charge will accumulate on the top of the bar. (2) The bar will not becomes polarized. (3) Positive charge will accumulate on the right end of the bar. (4) Negative charge will accumulate on the top of the bar.

You look at the voltmeter and find that the reading on the meter is -5脳10-4volts. (i) What can you conclude from this observation? (Remember that a voltmeter gives a positive reading if the positive lead is attached to the higher potential location.) (1) There is not enough information to figure out the sign of the mobile charges. (2) The mobile charges are negative. (3) The mobile charges are positive.
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