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Force of one dipole on another; non-symmetric

  1. Nov 5, 2011 #1
    1. The problem statement, all variables and given/known data
    The dipole p1 lies on the z axis at the origin. p2 is at a distance r away . Using cylindrical coordinates, p2 is at angle θ down from the z axis (see diagram), and points in the z direction. r is assumed to be much greater than d (distance between charged ends of dipole) therefore are evaluated as pure dipoles. I need to find the force of p1 on p2.
    The question encourages us to refer back to the derivation of the formula: F=(p[itex]\cdot[/itex][itex]\nabla[/itex])E

    2. Relevant equations
    V=(p1cosθ)/(4∏ε0r2)
    E(r,θ)=-[itex]\nabla[/itex]V(r,θ)

    3. The attempt at a solution
    There is no dependence on ∅.
    The E-field by the potential is:
    E(r,θ)=|p|/(4∏ε0r3)(2cosθ[itex]\hat{r}[/itex]+sinθ[itex]\hat{θ}[/itex])
    I'm just unsure of how to solve this. Do I multiply the |p|/(4∏ε0r3) component into the (2cosθ[itex]\hat{r}[/itex]+sinθ[itex]\hat{θ}[/itex]) and then take the gradient of that beast? Just point me in the right direction please! :)
     

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  2. jcsd
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