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 $11 μ m / s$ .

Step by step solution

Given information Part (a)

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

Explanation Part (a)

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

$\Rightarrow E = \frac{I}{σ A}$

The cross section area is a circle,

$E = \frac{I}{σ π r^{2}}$

$= \frac{4 I}{σ π d^{2}}$

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

$= 1.64 mV / m$

Final Answer Part (a)

The electric field is $1.64 mV / m$ .

Given information Part (b)

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

Explanation Part (b)

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

$= 1.1 \cdot 10^{- 5} m / s .$

$= 11 μ m / s$ .

Final answer Part (b)

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

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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

Step by step solution

Given information Part (a)

Explanation Part (a)

Final Answer Part (a)

Given information Part (b)

Explanation Part (b)

Final answer Part (b)

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

Short Answer

Step by step solution

Given information Part (a)

Explanation Part (a)

Final Answer Part (a)

Given information Part (b)

Explanation Part (b)

Final answer Part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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Study anywhere. Anytime. Across all devices.

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?