1. Limited time only! Sign up for a free 30min personal 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!

Biot-Savart law

  1. Aug 4, 2012 #1
    In the expression of Biot-Savart law
    B = (µo/4π) ∫ (I dl x r^)/r2
    why dl does not depend on the coordinate systems ?
    in books they are using del X dl = 0
     
  2. jcsd
  3. Aug 4, 2012 #2
    It's natural [itex]d\ell[/itex] doesn't depend on the coordinate system; it's a vector.

    Still, [itex]\nabla \times d\ell[/itex] doesn't make a whole lot of sense. Could you give some more context for this question?
     
  4. Aug 5, 2012 #3
    i am attaching a file in which the derivation of biot-savart law is given. Now after equation 6-29 they used del X dl' = 0. i want to know the reason
     

    Attached Files:

  5. Aug 5, 2012 #4
    It says the reason right in the screenshot:

    Here, [itex]d\ell[/itex] and [itex]d\ell'[/itex] are two different things. The first depends on "unprimed" coordinates (i.e. [itex]x, y, z[/itex]) and the second depends on "primed" coordinates [itex]x', y', z'[/itex]). The operator [itex]\nabla[/itex] differentiates only with respect to the unprimed coordinates. Hence, [itex]\nabla \times d\ell'[/itex] is zero because [itex]x', y', z'[/itex] are not functions of [itex]x,y, z[/itex]; they can't be differentiated with respect to the unprimed coordinates.

    This use of primed and unprimed variables is pretty common in proofs of integral theorems, particularly when you have a function on the left that is, say, [itex]X(r)[/itex], generally the variable of integration on the right is [itex]r'[/itex]. For example,

    [tex]E(r) = \int \frac{\rho(r')/\epsilon_0}{4\pi |r - r'|^2} \; dV'[/tex]

    Here, [itex]r'[/itex] is the dummy variable of integration, and [itex]dV'[/itex] is the associated volume element for that variable.
     
  6. Aug 5, 2012 #5
    now i got it. thanks a lot
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook