Mathematical problem in electrial/magnetic fields

[Niltiac]

Homework Statement

A charged particle moves in a region of space where there is a uniform magnetic field B (in the z direction say,) and a uniform electric field E in the yz plane. Write the equations of motion for the particle. Then solve them, taking for initial conditions (at t=0) x=y=z=0; xdot=xdot₀, ydot=zdot=0. Show that there is a drift velocity equal to E_y/B in the positive x direction. If E_y=0, then the orbit becomes a spiral about a line parallel to the z axis.

Homework Equations

The Attempt at a Solution

I've got one equation of motion:
dV/dt=q/m[(E_x+V_yB)xhat + (E_y-v_xB)yhat + E_zzhat] However the problem asks for equations (plural) and I'm only finding this one.

 

[George Jones]

The Attempt at a Solution

I've got one equation of motion:
dV/dt=q/m[(E_x+V_yB)xhat + (E_y-v_xB)yhat + E_zzhat] However the problem asks for equations (plural) and I'm only finding this one.

You have written one vector equation that is equivalent to three scalar equations, one for each direction. Write down these equations separately.

 

[Niltiac]

So the equations would be:
dV/dt_x= q/m(E_x+V_yB)
dV/dt_y=q/m(E_y-V_xB)
dV/dt_z=qE_z/m
?
Also, my instinct says that E_x should be zero since the electric field exists in the yz plane. Is this correct?

 

[George Jones]

Yes, this seems OK.