# The Ultimate problem!

A particle with specific charge $$\text{q/m}$$ moves in the region of space where there are uniform mutually perpendicular electric and magnetic fields with strength E (along $$y$$ axis) and magnetic field B (along $$z$$-axis). It had zero initial velocity and was located at the origin. For non-relativistic case, find the law of motion $$x(t)$$ and $$y(t)$$ of the particle and hence, the shape of the trajectory.

Define
- $$P$$ as the ratio of the area of the figure made with the $$x$$-axis when it again touches the $$x$$-axis,
- $$Q$$ as the length of the "arch" of that section of the figure,
- $$R$$ as the angular speed at which it reaches.

If the value of $$\frac{P}{Q\times R}$$ equals to

$\displaystyle \frac{a\pi {m}^{b}{E}^{c}{q}^{d}{B}^{e}}{f}$

give your answer as $$\displaystyle a + b + c + d + e + f$$.

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