Question is E=(x,y,z) B=(x,y,z) v=(x,y,z) (in vector form)
For all E,B,v find v(t) and r(t) v and r of course have their vector arrows.
F=ma= qE + qv x B
There is a hint to take second derivatives across and some terms will clear up. I was thinking more about the integrating it back to velocity and position functions.
The Attempt at a Solution
dv/dt - (q/m)v x B= qE
so VxB = (VyBz-VzBy)i-(VxBz-VzBx)j+(VxBy-VyBx)k
dvx/dt - q/m(VyBz-VzBy) = q Ex
So I got the cross product, and put the Lorentz equation in to its differentiate form, but I am stuck here since I don't understand what I am supposed to do when the question is asking "for all v(t) and r(t)". I guess I am more stuck on the format of the answer, like how is it supposed to look like, or how many vectors/equations there needs to be by the time I am done. At the end am I supposed to get just two equations that are the derivative/integral of each other that describe the position and velocity of any given charge if data plugged in right? I would assume so since it is all analytic.
Appreciate the help.