How Do You Calculate Current Density in a Wire?

AI Thread Summary
To calculate the current density in a wire, the formula J = i / A is used, where J is current density, i is current, and A is cross-sectional area. In this case, the wire has a diameter of 5.10 mm and carries a current of 28.5 A. The initial attempt incorrectly calculated the area using the circumference instead of the correct formula for the area of a circle. The correct cross-sectional area should be calculated using the diameter to find the radius, then applying the area formula A = πr². After clarifying the terms and calculations, the correct current density can be determined.
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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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