How Do You Calculate Current Density in a Wire?

[123yt]

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.

 

[berkeman]

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...

 

[berkeman]

Also, the units for resistivity are not meters...

 

[123yt]

Yeah, sorry, copy and pasted the question weirdly.

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