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Chapter 27: Q. 21 (page 762)

21. A 0.0075V/m electric field creates a 3.9mA current in a 1.0-mm-diameter wire. What material is the wire made of?

Short Answer

Expert verified

The material is the wire made of Nichrome.

Step by step solution

01

Given information

The electric field in the wire is 0.0075V/m.The current through the wire is 3.9mA. The diameter of the wire is 1.0-mm-diameter wire.

So, the radius isr=0.5mm=5×10-4m.

02

Explanation

Determine the material from its conductivity σ by,
J=σE(1)
whereJ=Iπr2is the current density . That means the current per square meter passing through a cross section of the wire -- andE is the electric field strength in the material.
Plugging the formula for the current density into equation (1) and solving for σ,
σ=IEπr2(2)

03

Explanation

The Calculation: Now we can simply plug these values into equation (2):σ=IEπr2
=3.9×10−3A(0.0075V/m)π5×10−4m2

=6.6×105Ω−1×m−1

The only material with a conductivity near6.6×105Ω-1×m-1 is Nichrome.
04

Final answer

The material the wire is made from Nichrome.

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