Finding current from current density of wire

In summary, the conversation discusses how to find the total current in a cylindrical wire with a given current density. The method involves integrating over the area and dealing with the 'z' direction. The conversation also includes a mistake in the calculations and the correct method for evaluating the integrals.
  • #1
maherelharake
261
0

Homework Statement



A cylindrical wire of radius 3mm has current density, J=3s |φ-[tex]\pi[/tex]| z_hat. Find the total current in the wire.


Homework Equations





The Attempt at a Solution


I believe all I have to do is integrate over the area, but for some reason I can't get it to work. Is the differential area going to be da=s ds dφ? In that case s goes from 0 to 3mm and φ goes from 0 to 2Pi? The 'z' direction is throwing me off a bit. Thanks.
 
Physics news on Phys.org
  • #2
Yes, that's right. Post your work if you still can't get it to work out so we can see where you're going wrong.
 
  • #3
I just tried to work it out on a napkin, because I am not near a scanner at the moment. I ended up with a net result of 0 though. If you don't think this is correct, I can try to rewrite it and take a picture with my phone and upload it. Thanks again.
 
  • #4
maherelharake said:
I just tried to work it out on a napkin, because I am not near a scanner at the moment. I ended up with a net result of 0 though. If you don't think this is correct, I can try to rewrite it and take a picture with my phone and upload it. Thanks again.

Yes, please upload it. Or you could use the Latex editor in the Advanced Reply window to write out your equations. Click on the [tex]\Sigma[/tex] symbol to the right in the toolbar to see your Latex options.
 
  • #5
Alright here you go. If you can't read it, let me know. Thanks.
http://i77.photobucket.com/albums/j72/maherelharake/photo-31.jpg
 
  • #6
You're not dealing with the absolute value correctly. Break the integral over the angle into two ranges, one from 0 to π and the other from π to 2π. For the first integral, |φ-π|=-(φ-π), and for the other, |φ-π|=φ-π.
 
  • #8
Your integrals look fine, but you made a mistake somewhere evaluating them.
 
  • #9
Hmm I can't find it. I checked it a few times after I posted it. Did you work it out and get a different result?
 
  • #10
I entered it into Mathematica and got a different result. It looks like you messed up the angular integrations in several spot. Every integral should be proportional to π2, but you have π, π2, and π3.

You can simplify the algebra a bit by separating the s integral and φ integral:

[tex]I=\int_0^{R} 3s^2ds \int_0^{2\pi} |\varphi-\pi|\,d\varphi[/tex]

and using the substitution u=φ-π to do the angular integrals.
 
  • #11
I seem to have gotten R3 Pi2where R=3 mm. Am I close? And of course, the answer is in Amps. Thanks.
 
  • #12
Yup, that matches what I got.
 
  • #13
Ok thanks.
 

1. What is current density?

Current density refers to the amount of electric current flowing through a given area of a material. It is measured in amperes per square meter (A/m^2).

2. How is current density related to current?

Current density and current are directly proportional. This means that as current density increases, the amount of current flowing through a material also increases.

3. How do you find current from current density of a wire?

To find current from current density of a wire, you need to know the cross-sectional area of the wire and the value of the current density. The current can then be calculated by multiplying the cross-sectional area by the current density.

4. What factors affect current density in a wire?

The current density in a wire can be affected by the material of the wire, its length and cross-sectional area, and the voltage applied to it. The temperature of the wire can also affect its conductivity and thereby affect the current density.

5. How is current density relevant in practical applications?

Current density is important in understanding the behavior and limitations of electric circuits and materials. It is also used in designing and optimizing electrical systems, such as in the development of power transmission lines and electronic devices.

Similar threads

  • Advanced Physics Homework Help
Replies
2
Views
971
  • Advanced Physics Homework Help
Replies
5
Views
984
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
8
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
6
Views
3K
  • Electromagnetism
Replies
5
Views
857
  • Advanced Physics Homework Help
Replies
4
Views
1K
Back
Top