(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...

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# Homework Help: Expressing equation of motion in Cartesian components

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