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!

Homework Help: Using stokes theorem to find magnetic field

  1. May 10, 2010 #1
    1. The problem statement, all variables and given/known data

    magnetic field is azimuthal B(r) = B(p,z) [tex]\phi[/tex]
    current density J(r) = Jp(p,z) p + Jz(p,z) z
    = p*exp[-p] p + (p-2)*z*exp[-p] z

    use stokes theorem to find B-filed induced by current everywhere in space

    2. Relevant equations

    stokes - {integral}dS.[curl A] = {closed integral}dl.A
    curl B(r) = J(r)

    3. The attempt at a solution

    ={integral}dS.[curl B(r)] = {closed integral}dl.B(r)
    ={integral}dS.J(r) = {closed integral}dl.B(p,z) [tex]\phi[/tex]

    {integral}dS.J(r) = {integral}dS.p*exp[-p] p + (p-2)*z*exp[-p] z = {closed integral}dl.B(p,z) [tex]\phi[/tex]

    dl = pd[tex]\phi[/tex] [tex]\phi[/tex]
    dS = pd[tex]\phi[/tex]dz p + pd[tex]\phi[/tex]dp z

    {closed integral}pd[tex]\phi[/tex].B(p,z) [tex]\phi[/tex] - with limits 0-2pi
    = B(p,z)*2pi*p

    {integral}dS.p*exp[-p] p + (p-2)*z*exp[-p] z
    do in 2 parts:
    {integral}pd[tex]\phi[/tex]dz.p*exp[-p] p - with limits 0-2pi and 0-R
    = 2pi*p2*R*exp[-p]

    {integral}pd[tex]\phi[/tex]dp.(p-2)*z*exp[-p] - with limits 0-2pi and 0-r
    = -2pi*r2*exp[-r]

    so B(p,z)*2pi*p = 2pi*p*R*exp[-p] - 2pi*r2*exp[-r]
    = B(p,z) = p*R*exp[-p] - r2/p*exp[-r]

    is this answer right?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. May 10, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    What's the difference between R, r, and p (by which I think you mean ρ)? That's the first thing you need to clear up.

    You didn't say what surface S you're integrating over. In any case, I think your evaluation of

    [tex]\oint_S (\nabla\times\textbf{B})\cdot d\textbf{S}[/tex]

    is incorrect.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook