Chapter 27: Q. 15 (page 762)

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

Short Answer

Expert verified

The current density in the wire is $4.2 \times 10^{6} A / m$ .

Step by step solution

Given information

A hollow copper wire's inner diameter is $d = 1.0 mm$ and an outer diameter is $2.0 mm$ carries a current of $10 A$ .

Explanation

The area of the wire is calculated by the area of the outer circle with diameter $D = 2.0 mm$ minus the area of the inner circle $d = 1.0 mm$ . Hence,
$A = \frac{1}{4} π D^{2} - \frac{1}{4} π d^{2}$

$= \frac{1}{4} π (D^{2} - d^{2})$

The current density $j$ is given by the current $I = 10 A$ divided by area of circle localid="1648796043058" $A = \frac{1}{4} π (D^{2} - d^{2})$

So,

$j = \frac{I}{A} = \frac{4 I}{π (D^{2} - d^{2})}$

localid="1648796295327" $= 4.2 \times 10^{6} A / m^{2}$

Final Answer

The current density in the wire is $4.2 \times 10^{6} A / m$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Given information

Explanation

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Space Physics

Medical Physics

Engineering Physics

Physics of Motion

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

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

Step by step solution

Given information

Explanation

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Space Physics

Medical Physics

Engineering Physics

Physics of Motion

Further Mechanics and Thermal Physics

Study anywhere. Anytime. Across all devices.

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