How Do You Calculate Current Density in a Wire?

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Homework Help Overview

The discussion revolves around calculating the current density in a wire with a circular cross-section, given its diameter and the current it carries. The problem involves understanding the relationship between current, area, and current density.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula for current density and the correct interpretation of the wire's dimensions. There are attempts to calculate the current density using the current and area, but confusion arises regarding the definitions of diameter, area, and circumference.

Discussion Status

The discussion includes corrections regarding the use of terms and units, with some participants providing clarifications on the definitions involved. There is acknowledgment of errors in the initial calculations, and one participant indicates they have resolved their confusion.

Contextual Notes

Participants note that the diameter was misinterpreted in calculations, and there was a misunderstanding regarding the units for resistivity. The original poster's approach to calculating the area was also questioned.

123yt
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Homework Statement


A long straight wire with circular cross-section and a diameter of 5.10 mm is made of a metal with resistivity = 5.00×10-8 m. The wire carries a current of 28.5 A. Calculate the current density in the wire.


Homework Equations


J = i / A


The Attempt at a Solution


I took the surface area, 0.0051 m, and multiplied it by pi to get the circumference. Then, I divided the current by the circumference and got 1778.79 A/m^2.

It's incorrect.
 
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123yt said:

Homework Statement


A long straight wire with circular cross-section and a diameter of 5.10 mm is made of a metal with resistivity = 5.00×10-8 m. The wire carries a current of 28.5 A. Calculate the current density in the wire.


Homework Equations


J = i / A


The Attempt at a Solution


I took the surface area, 0.0051 m, and multiplied it by pi to get the circumference. Then, I divided the current by the circumference and got 1778.79 A/m^2.

It's incorrect.

5.1mm is the diameter, not the area, so multiplying it by PI does indeed give you the circumference. But circumference is not the area.

Please try again, and get your terms for diameter, area, and current density (current divided by the cross-sectional area) correct...
 
Also, the units for resistivity are not meters...
 
Yeah, sorry, copy and pasted the question weirdly.

Anyways, thanks for the correction. I got it figured out now.
 

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