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Homework Help: Torque on/due to dipoles.

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Two dipoles as in pic below a distance r apart, find the torque applied to each dipole due to the other.
    [tex]\uparrow1 ------------2\rightarrow[/tex]

    2. Relevant equations
    [tex]\itshape \vec{p}=p(cos\:\theta \hat{r}-sin\:\theta\hat{\theta})[/tex]
    [tex]\itshape \vec{E}=\frac{p}{4\pi\epsilon_{0}r^{3}}\: (2cos\:\theta\hat{r}+sin\:\theta\hat{\theta})[/tex]
    [tex]\itshape \vec{N}=\vec{p}\:X\:\vec{E}[/tex]

    3. The attempt at a solution
    well i only am concerning myself with the non constants in the cross product.
    [tex]\itshape \vec{N}=\vec{p_{2}}\:X\:\vec{E_{1}}[/tex]
    [tex]\itshape (cos\:\theta\hat{r}-sin\:\theta\hat{\theta})X(2cos\:\theta\hat{r}+sin\:\theta\hat{\theta})[/tex]
    ok this is where i am confused... do i use \theta as angle under the z axis for the direction the dipole and electric field are pointing, or do i use them for angles of separation or what? if i use them for angle under the z axis for the vector it is pertaining to i get the torque will be [tex]-3cos\:\theta sin\:\theta sin \:\phi\hat{i}+3cos\:\theta sin\:\theta cos \:\phi\hat{j}[/tex], which applying angles under z axis is 0. But that isn't what the answer should be.
  2. jcsd
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