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: Vector Potential

  1. Mar 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Compute the vector potentials for the following two-dimensional fields:

    [tex]\vec{F}[/tex] = [tex]\frac{xy\vec{i}}{1}[/tex] - [tex]\frac{y^{2}\vec{j}}{2}[/tex]


    2. Relevant equations
    (1)[tex]\int^{1}_{0} t \vec{F}\times \frac{d\vec{r}}{dt} dt[/tex]


    3. The attempt at a solution
    I solved this problem a different way, but my problem is using the above formula. The way that i did it was as follows:

    [tex]\vec{k} \times [/tex][tex]\vec{F}[/tex] = [tex]\nabla\chi[/tex] = [tex]\left\langle\frac{y^{2}}{2},xy,0\right\rangle[/tex]

    so [tex]\chi[/tex] = [tex]\frac{xy^{2}}{2}[/tex]

    but, [tex]\vec{G} = \vec{k}\chi=\frac{xy^{2}}{2}\vec{k}[/tex]
    where [tex]\vec{F} = \nabla \times \vec{G}[/tex]

    This is the correct answer given by the book, with G being the vector potential. However, I cannot get to this answer using the formula (1) that I gave above. I did the following:

    [tex]\vec{r}=t\left\langle x,y,z\right\rangle[/tex]
    [tex]\frac{d\vec{r}}{dt}=\left\langle x,y,z\right\rangle[/tex]
    [tex]\vec{F}(\vec{r}(t)) = \left\langle xyt^{2},\frac{t^{2}y^{2}}{2},0\right\rangle[/tex]

    Then, following through with the computations I get an incorrect answer. Did i set this up incorrectly? Any help at all would be greatly appreciated
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Loading...
Similar Threads for Vector Potential Date
Fourier transform of vector potential Nov 3, 2015
Thin Rod Gravitational Potential and Field Vector Jun 19, 2015
Vector curl problem and potential Apr 11, 2015
Curl of the vector potential Mar 14, 2014