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Chapter 27: Q. 20 (page 762)

20. What electric field strength is needed to create a 5.0Acurrent in a 2.0-mm-diameter iron wire?

Short Answer

Expert verified

The electric field strength is needed to create a 5.0Acurrent in a

2.0-mm-diameter iron wire is 0.159V/m.

Step by step solution

01

Given information

A 5.0 current in a 2.0-mm-diameter iron wire with the electric field strength.

02

Explanation

The current density is given by the electric field and the conductance as, J=σE

The current density J=IAas,

⇒Iπr2=4Iπd2

Substituting the two expressions for the current density,

σE=4Iπd2

The electric field Eto be,

E=4Iπσd2

E=4×5π×1×107×0.0022

=0.159V/m
03

Final answer

The electric field strength is needed to create a 5.0Acurrent in a

2.0-mm-diameter iron wire is 0.159V/m.

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Most popular questions from this chapter

A 0.60-mm-diameter wire made from an alloy (a combination of different metals) has a conductivity that decreases linearly with distance from the center of the wire: σ(r)=σ0-cr, with σ0=5.0×107Ω-1m-1and c=1.2×1011Ω-1m-2. What is the resistance of a 4.0mlength of this wire?

15. A hollow copper wire with an inner diameter of 1.0mmand an outer diameter of 2.0mm carries a current of 10A. What is the current density in the wire?

The starter motor of a car engine draws a current of 150Afrom the battery. The copper wire to the motor is 5.0mmin diameter and 1.2mlong. The starter motor runs for 0.80suntil the car engine starts.

a. How much charge passes through the starter motor?

b. How far does an electron travel along the wire while the starter motor is on?

The electron drift speed in a wire is exceedingly slow-typically only a fraction of a millimeter per second. Yet when you turn on a flashlight switch, the light comes on almost instantly. Resolve this apparent paradox.

a. How long must a 0.60mmdiameter aluminum wire be to have a 0.50Acurrent when connected to the terminals of a 1.5Vflashlight battery?

b. What is the current if the wire is half this length?
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