(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The general equation of motion of a non-relativistic particle of mass m and charge q when it is placed in a region where there is a magnetic field B and an electric field E is

[tex]m\bold{\ddot{r}} = q(\bold{E} + \bold{\dot{r}} \times \bold{B}) [/tex]

where r is the position of the particle at time t and [tex]\bold{\dot{r}} = v_o \bold{k}[/tex]

Write the above equation in terms of Cartesian components of the vectors involved.

When [tex]\bold{B} = B \bold{j}[/tex] and [tex]\bold{E} = E \bold{i}[/tex] and the particle starts from the origin at t=0 and [tex]\bold{\dot{r}} = v_o \bold{k}[/tex], prove that the particle continues along its initial path.

There's a further third part which is even more complicated, but I'm trying to wrap my head around the first two.

2. The attempt at a solution

I'm definitely missing something here that I should know but don't.

[tex]\dot{\bold{r}} \times \bold{B} = -Bqv_o \bold{i}[/tex]

[tex]\bold{E} = E \bold{i}[/tex]

Given these, shouldn't [tex]m\ddot{x} = qE - Bv_{o}q[/tex]? And shouldn't the rest be effectively zero because both E and the cross vector only have values in the i direction!

The answer given is this:

[tex]m\ddot{x} = -\frac{(Bq)^2}{m}x + qE - Bv_{o}q[/tex]

[tex]\ddot{y} = 0[/tex]

No answer for [tex]\ddot{z}[/tex] is given.

I'd appreciate any hints, please don't work everything out for me...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Expressing equation of motion in Cartesian components

**Physics Forums | Science Articles, Homework Help, Discussion**