I have a constant magnetic field pointing in the direction of the z axis and I'm supposed to find a formula for the way an electron with arbitrary starting position and velocity would travel in this field. The formula in this case would be F(x, x', t) = q(v × B(x, t)) and I'm stuck at the point where I have to split this formula into the three equations for motion. Would I just use F(x, x', t) = q(x' × B(x, t)) and so on or am I missing something? And how would I proceed afterwards? Then there's also a similar problem, but with an electrical field pointing in the direction of the y axis. Which formula would I use here? The only one I can think of is F = q*E, but don't I need a formula that contains information about the particle involved?