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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

Expert verified

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

(b) The electron drift speed in the wire is 11μm/s.

Step by step solution

01

Given information Part (a)

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

02

Explanation Part (a)

To find the current density, equating the two expressions,
σE=J=IA

⇒E=IσA

The cross section area is a circle,

E=Iσπr2

=4Iσπd2

E=4×0.02Aπ×6.2×107×0.00052m

=1.64mV/m

03

Final Answer Part (a)

The electric field is 1.64mV/m.

04

Given information Part (b)

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

05

Explanation Part (b)

To solve for the drift speed as
vd=4IÏ€d2ene
In the numerical case,
vd=4×0.02Aπ×0.00052m×1.6×10-19×5.8×1028

=1.1·10-5m/s.

=11μm/s.

06

Final answer Part (b)

The electron drift speed in the wire is 11μ³¾/s.

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