What affects the particle first? I just want to check my reasoning. We have a particle starting at the origin with 

$$v(0)=\frac{E}{B}\hat y$$

There is a magnetic field pointing in the $\hat x$ direction and an electric field pointing in the $\hat z$ direction. What happens right after $t=0$?
I think one of these 3 things will happen:


*

*If the magnetic field affects the particle first, then it will initially start to curve downwards.

*If the E-field affects the particle first, then it will initially curve upwards.

*If both fields affect the particle initially, then I think the particle will move in a straight line from the origin along the $y$-axis.
 A: Option 1 and 2 are only valid when one of the fields is turned on before the other so that it affects the charged particle first.
Otherwise, option 3 is the correct one. Particle travels with the same velocity, undeflected
Explanation
The thing is  we just have to check for the force acting on the particle at any instant. The electric field will exert a force $F_E$ = $qE\hat{z}$ in the positive $z$ direction
The magnetic field will exert a force $F_B$ given by -
$F_B$ = $q\vec{v}\times\vec{B}$ = $q\frac{E}{B}\hat{y}\times B\hat{x}$ = $-qE\hat{z}$ 
This, as you can see is time independent, meaning no matter which instant of time you look at, you will see $F_E$ = $-F_B$.....cancelling each other perfectly. So the particle will move unfettered. Had there been an imbalance of force at any point of time, we would have seen cycloidal motion. But not here!
A: If both the electric and the magnetic field are present at the start and the given velocity in y-direction is $v(0)= E/B$, then the magnetic Lorentz force component $q\vec v×\vec B$  directed in negative z-direction has the same strength as the electric field force $q\vec E$ directed in positive z-direction. Thus the magnetic and electric field forces compensate each other and the particle will fly with constant velocity $v=v(0)$ along the y-axis.
