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Chapter 27: Q. 15 (page 762)

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?

Short Answer

Expert verified

The current density in the wire is 4.2脳106A/m.

Step by step solution

01

Given information

A hollow copper wire's inner diameter is d=1.0mmand an outer diameter is 2.0mmcarries a current of 10A.

02

Explanation

The area of the wire is calculated by the area of the outer circle with diameterD=2.0mmminus the area of the inner circle d=1.0mm. Hence,
A=14蟺D2-14蟺d2

=14蟺D2-d2

The current density jis given by the current I=10Adivided by area of circle localid="1648796043058" A=14蟺D2-d2

So,

j=IA=4I蟺D2-d2

localid="1648796295327" =4.2脳106A/m2

03

Final Answer

The current density in the wire is 4.2脳106A/m.

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