1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sources of Magnetic Field

  1. Oct 16, 2006 #1
    the question is that:

    A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is [itex] \vec J[/itex]. The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relation

    (the relation is in the attachment)

    where a is the radius of the cylinder, r is the radial distance from the cylider axis, and [itex]I_0[/itex] is a constant haveing units of amperes.
    a) show that [itex]I_0[/itex] is the total current passing through the entire cross section of the wire.
    b). Using Ampere's law, derive an expression for the magnitude of the magnetic field [itex]\vec B[/itex] in the region r>=a .
    c). Obtain an expression for the current I contained in a circular cross section of radius r<=a and centered at the cylinder axis.
    d). Using Ampere's law, derive an expression for the magnitude of the magnetic field [itex]\vec B[/itex] in the region r<=a.


    For a, Since for the entire cross section of the wire, i subt. r=a into the relation. But it will give zero. I shown nothing. If I subt. J=I/A,
    then [itex]I=2 I_0 [1- (\frac{r}{a})^2][/itex]. Anything wrong,
    and how to proof that?
     

    Attached Files:

    Last edited: Oct 16, 2006
  2. jcsd
  3. Oct 16, 2006 #2

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    Since the current density is not constant, you need to integrate over the cross section.

    Also, have you taken a look at the LaTeX tutorial? If you post the question that way, you won't need to wait till the attachment is approved.
     
  4. Oct 16, 2006 #3
    i am sorry since i do not familiar that tutorial yet........

    Should i integrate [itex]\frac{2 I_0}{\pi a^2} [1- (\frac{dr}{a})^2][/itex]
    from 0 to a? if yes, how to integerate [itex](dr)^2[/itex]
     
    Last edited: Oct 16, 2006
  5. Oct 16, 2006 #4

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    No, that's completely wrong.

    If you take a small elemental area da, then the current which flows through that bit is [tex]\vec{J}.\vec{da}[/tex]

    To find the net current through the whole wire, in a sense you add up the current through all the small elemental areas.
    So your net current will be

    [tex]I=\int \vec{J}.\vec{da} [/tex]

    Now,
    (i) Can you tell me what elemental area you will take?
    (ii) What will the limits of integration be?
     
    Last edited: Oct 16, 2006
  6. Oct 17, 2006 #5
    elemental area is the small cross section area [itex]dA=2 \pi r da[/itex],
    and the limits of integration is from 0 to a?
     
    Last edited: Oct 17, 2006
  7. Oct 17, 2006 #6
    I have got the ans.
    and the following problems are also be solved,
    thank you so much
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Sources of Magnetic Field
  1. Magnetic field (Replies: 4)

  2. Magnetic Field (Replies: 0)

Loading...