Using Current Density to find Total Current

  • Thread starter slavito
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Homework Statement



Suppose a wire has a radius [itex] R[/itex] and a current density of [itex]J = I_0 \frac{x^2} {R^4}\hat{k}[/itex]. Taking the wire to have cylindrical geometry, calculate the total current flowing down the wire, defined as [itex]I = \int J \cdot \vec{dA} [/itex].


Homework Equations


[itex]J = I_0 \frac{x^2} {R^4}\hat{k}[/itex]
[itex]I = \int J \cdot \vec{dA} [/itex]


The Attempt at a Solution



Here, I assumed that dA = R dR dx . I then attempted to do the Integral. I assumed Io was a constant, so I pulled that out of the Integral, giving me...

[itex]I = I_o\int x^2\cdot \vec{dx} \int R^{-3} \cdot \vec{dR} [/itex]

Evaluating, I got...

[itex]I = I_o\frac{x^3}{3}\frac{R^{-2}}{-2}\hat{k}[/itex]

I have no idea if this is right or wrong. I don't even know if I'm on the right track. Please, any sort of help you could give me would be greatly appreciated!
 

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi slavito! welcome to pf! :smile:

i don't understand what x is :confused:

does x mean distance from the centre (which we would usually call "r")?

or is x one of the usual x,y,z coordinates (with the wire pointing along the z axis)?

(and R is a constant, so you can't have dR)
 
  • #3
rude man
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Assuming the wire axis and the current run along the z axis and the wire axis is centered at x=y=0:

what is a sliver of area of width dx and height = distance between 2 points on the circle at x? What is then the current within that area?

Tiny-tim is of course right about R and he's right about the need to define your problem fully. Most posters for some reason don't post the problem as handed to them.
 

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