The trajectory of the particle with E=(0,0,E) and B=(B,0,0)

I am trying to produce the trajectory of the charged particle in $$E=(0,0,E)$$ and $$B=(B,0,0)$$. The relevant equations are: $$y(t) = \frac{E}{\omega B}(\omega t - \sin{\omega t}), \quad z(t) = \frac{E}{\omega B}(1 - \cos{\omega t})$$

This is from Griffiths, D, Introduction to Electrodynamics. I was looking to get a figure looking like this:

The code that I wrote was

ClearAll["Global*"]
Velocity = 2.0 10^4;
BField = 100 10^-9;
EField = Velocity*BField;
w = 4;
ParametricPlot3D[{0, EField/(w BField) (w t - Sin[w t]),
EField/(w BField) (1 - Cos[w t])}, {t, 0, 3},
PlotStyle -> {Directive[Blue, Dashed]}, AxesLabel -> {x, y, z},
LabelStyle -> Directive[Blue, Bold], ViewPoint -> Right,
ImageSize -> Large]


This gives a plot which looks like:

Even though the features are the same, this does not like the one that I am planning to reproduce.

Could anybody let me know, what am I doing wrong? Thanks in advance

We can also draw the frame manually.

ClearAll["Global*"]
Velocity = 2.0 10^4;
BField = 100 10^-9;
EField = Velocity*BField;
w = 4;
plot = ParametricPlot3D[{0, EField/(w BField) (w t - Sin[w t]),
EField/(w BField) (1 - Cos[w t])}, {t, 0, 2 \[Pi]},
PlotStyle ->
Arrowheads[{{.03, 1/8 + .02}, {.03, 3/8 + .02}, {.03,
5/8 + .02}, {.03, 7/8 + .02}}]] /. Line -> Arrow;
{{xmin, xmax}, {ymin, ymax}, {zmin, zmax}} =
PlotRange /. AbsoluteOptions[plot, PlotRange];
frame = Graphics3D[{Black,
Arrow[Tube@{1.2 {0, ymin, 0}, 1.2 {0, ymax, 0}}],
Arrow[Tube@{{0, 0, 0}, {50000, 0, 0}}],
Arrow[Tube@{1.2 {0, 0, zmin}, 2 {0, 0, zmax}}]}];
Show[plot, frame, ViewPoint -> {1, 0.2, .2},
ViewProjection -> "Orthographic", PlotRange -> All,
AxesEdge -> {{1, -1}, {1, -1}, {1, -1}},
Boxed -> {Front, Bottom, Left}]


The numerical values for B making it hard to visualize since it is so small. How about

Velocity = 2.0 10^4;
B0 = 10000;
E0 = Velocity*B0;
w = 4;
z[t_] := E0/(w B0) (1 - Cos[w t])
y[t_] := E0/(w B0) (w*t - Sin[w t])

ParametricPlot3D[{B0, y[t], z[t]}, {t, 0, 6},
AxesLabel -> {"x", "y", "z"}, BaseStyle -> 14,
PlotRange -> {{0, B0}, Automatic, Automatic},
ViewPoint -> {1, 1, 1}, ImageSize -> 300, SphericalRegion -> True]


Then use the mouse to change the view point/angle?