# Kinematics of a dipole - Wopho Problem

1. Jan 3, 2014

### jaumzaum

This problem is originally from Wopho and its goal is to describe the trajectory of a point mass charge around a dipole.

http://img18.imageshack.us/img18/2676/fvac.png [Broken]

First we have to calculate the radial and tangential electric fields made by the dipole (this I've done as well) but when it asks about the trajectory I get confused

I've calculated the radial electric field Er = 2kqd cosθ/R³ and the tangential electric field Et = kqd sinθ/R³

From this I get the following:
Let B = kQqd/m

$\frac{d^{2}R}{dt^{2}} = \frac{2B cosθ}{R^{3} }$

$\frac{d^{2}θ}{dt^{2}} = \frac{B sinθ}{R^{4} }$

R initial = D
θ initial = 0
dR/dt initial = 0
dθ/dt initial = V/D

How do I find R(t), θ(t) or R(θ)?

[]'s
John

Last edited by a moderator: May 6, 2017
2. Jan 3, 2014

### Staff: Mentor

"describe" or "calculate"? Calculating looks more complicated than the Kepler problem - it could be possible (I don't know), but I would be surprised if there is an easy solution.

3. Jan 4, 2014

### rude man

The trajectory depends on the initial conditions of the charge. What are they?

Other than that I see no particular problem: F = ma with F = qE, E = electric field of a dipole. Set up a coordinarte system with the dipole center at the origin and the dipole direction along the x axis. Write x and y equations. I haven't done the math so maybe that's a challenge.

Last edited: Jan 4, 2014
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