A charged particle travels in a gravity-free space without any...

The net force on a charged particle in an electric and magnetic field is given by the Lorentz force:

$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$

For the particle to travel without any change in velocity, the net force must be zero, i.e., $\vec{F} = 0$.

If $E = 0$ and $B = 0$, then $\vec{F} = 0$. This is possible.

If $E = 0$ and $B \neq 0$, then $\vec{F} = q(\vec{v} \times \vec{B})$. If the particle moves parallel or anti-parallel to the magnetic field ($\vec{v} \parallel \vec{B}$), then $\vec{v} \times \vec{B} = 0$ and $\vec{F} = 0$. This is possible.

If $E \neq 0$ and $B \neq 0$, then $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$. If $\vec{E} = -(\vec{v} \times \vec{B})$, which happens when $\vec{E}$, $\vec{v}$, and $\vec{B}$ are mutually perpendicular and $E = vB$, then $\vec{F} = 0$. This is possible.

If $E \neq 0$ and $B = 0$, then $\vec{F} = q\vec{E} \neq 0$. The particle will accelerate, and its velocity will change. This is not possible.