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Electric deflection of an electron beam

Electrons are accelerated through a voltage $V_x$ towards a positively charged plate. Some of the electrons pass through a small hole in the plate and form and electron beam that travels to a region where an electric field is established by applying a voltage $V_y$ between two metal plates spaced a distance $d$ apart.

The electrons are accelerated from rest to the positively charged plate in a distance of 5 cm. The electrons get deflected as they pass through the electric field between the plates. In the plot below, the vertical axis has been expanded to show the deflection more clearly.

 

  

$V_x=$ 5000 [V]

$V_y=$ 1 [V]

$d=$ 0.05 [m]

 Numerical 6th order differential equation solver 

$ \large \frac{dx}{dt}=$

$v_x$

$ \large \frac{dv_x}{dt}=$

$ \large \frac{dy}{dt}=$

$v_y$

$ \large \frac{dv_y}{dt}=$

$ \large \frac{dz}{dt}=$

$v_z$

$ \large \frac{dv_z}{dt}=$

Initial conditions: 

$t_0=$

 

$\Delta t=$

$x(t_0)=$

 

$N_{steps}$

$v_x(t_0)=$

 

Plot:

vs.

$y(t_0)=$

 

$v_y(t_0)=$

 

$z(t_0)=$

 

$v_z(t_0)=$

 

 $t$   $x$   $v_x$   $y$   $v_y$   $z$   $v_z$