# Force of one dipole on another; non-symmetric

1. Nov 5, 2011

### mhryciw

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$\cdot$$\nabla$)E

2. Relevant equations
V=(p1cosθ)/(4∏ε0r2)
E(r,θ)=-$\nabla$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$\hat{r}$+sinθ$\hat{θ}$)
I'm just unsure of how to solve this. Do I multiply the |p|/(4∏ε0r3) component into the (2cosθ$\hat{r}$+sinθ$\hat{θ}$) and then take the gradient of that beast? Just point me in the right direction please! :)

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