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Chapter 27: Q. 23 (page 762)

23. A $0.50$ -mm-diameter silver wire carries a $20 mA$ current. What are (a) the electric field and (b) the electron drift speed in the wire?

Short Answer

Expert verified

(a) The electric field is $1.64 mV / m$ .

(b) The electron drift speed in the wire is $11 渭 m / s$ .

Step by step solution

01

Given information Part (a)

A $0.50$ -mm-diameter silver wire carries a $20 mA$ current in the electric field.

02

Explanation Part (a)

To find the current density, equating the two expressions,
$蟽 E = J = \frac{I}{A}$

$鈬� E = \frac{I}{蟽 A}$

The cross section area is a circle,

$E = \frac{I}{蟽蟺 r^{2}}$

$= \frac{4 I}{蟽蟺 d^{2}}$

$E = \frac{4 脳 0.02 A}{蟺脳 6.2 脳 10^{7} 脳 0 . 0005^{2} m}$

$= 1.64 mV / m$

03

Final Answer Part (a)

The electric field is $1.64 mV / m$ .

04

Given information Part (b)

A $0.50$ -mm-diameter silver wire carries a $20 mA$ current in the electron drift speed in the wire.

05

Explanation Part (b)

To solve for the drift speed as
$v_{d} = \frac{4 I}{蟺 d^{2} e n_{e}}$
In the numerical case,
$v_{d} = \frac{4 脳 0.02 A}{蟺脳 0 . 0005^{2} m 脳 1.6 脳 10^{- 19} 脳 5.8 脳 10^{28}}$

$= 1.1 路 10^{- 5} m / s .$

$= 11 渭 m / s$ .

06

Final answer Part (b)

The electron drift speed in the wire is $11 渭尘 / s$ .

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Most popular questions from this chapter

75. A $300 渭 F$ capacitor is charged to $9.0 V$ , then connected in parallel with a $5000 惟$ resistor. The capacitor will discharge because the resistor provides a conducting pathway between the capacitor plates, but much more slowly than if the plates were connected by a wire. Let $t = 0 s$ be the instant the fully charged capacitor is first connected to the resistor. At what time has the capacitor voltage decreased by half, to $4.5 V$ ?
Hint: The current through the resistor is related to the rate at which charge is leaving the capacitor. Consequently, you'll need a minus sign that you might not have expected.

17. What is the mean time between collisions for electrons in (a) an aluminum wire and (b) an iron wire?

A wire of radius $R$ has a current density that increases linearly with distance from the center of the wire: $J (r) = k r$ , where $k$ is a constant. Find an expression for $k$ in terms of $R$ and the total current $I$ carried by the wire.

74. FIGURE CP27.74 shows a wire that is made of two equal diameter segments with conductivities $蟽_{1}$ and $蟽_{2}$ . When current $I$ passes through the wire, a thin layer of charge appears at the boundary between the segments.
a. Find an expression for the surface charge density $畏$ on the boundary. Give your result in terms of $I, 蟽_{1}, 蟽_{2}$ , and the wire's cross-section area $A$ .
b. A $1.0$ -mm-diameter wire made of copper and iron segments carries a $5.0 A$ current. How much charge accumulates at the boundary between the segments?

II You need to design a $1.0 A$ fuse that "blows" if the current exceeds $1.0 A$ . The fuse material in your stockroom melts at a current density of $500 A / {cm}^{2}$ . What diameter wire of this material will do the job?

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