Homework Help: 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