# Force due to a Dipole

1. Apr 7, 2014

### moongate

I've been trying to answer the following question, without success. Can someone help me here?

A \lq\lq pure \rq\rq dipole is located at the origin and is directed to the +z-axis. a)Calculate the force on a point charge q at (0,a,0). b)Calculate the force on q if it is at (a,0,0). c)Calculate the work needed to move q from (0,a,0) to (a,0,0)

2. Apr 7, 2014

### dipole

Well first you'll want to calculate the potential and field due to a point dipole. The potential due to any arbitrary charge distribution can be written as,

$$\Phi(\vec{x}) = \frac{1}{4\pi\epsilon_0}\bigg[\frac{q}{r} + \frac{\vec{p}\cdot\vec{x}}{r^3} + \frac{1}{2}Q_{i,j}\frac{x_ix_j}{r^5} + \dots \bigg]$$

Which of these moments are non-zero for a pure dipole?

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