What is the behaviour of perpendicular electric field ${\rm{\vec E}}$ and magnetic field ${\rm{\vec B}}$ ?

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion

An electron enters with a velocity ${\rm{\vec v}},{{\rm{v}}_0}{\rm{\hat i}}$ into a cubical region (faces parallel to coordinate planes) in which there are uniform electric and magnetic fields. The orbit of the electron is found to spiral down inside the cube in plane parallel to the $\mathrm{xy}$ - plane. Suggest a configuration of fields $\mathrm{E}$ and $\mathrm{B}$ that can lead to it.

Give features of force on charge particle inside magnetic field.

A proton and an alpha particle of the same enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the circular paths described by the alpha particle and proton is ....

A particle of mass $m$ carrying charge $q$ is accelerated by a potential difference $V$. It enters perpendicularly in a region of uniform magnetic field $B$ and executes circular arc of radius $R$, then $\frac{q}{m}$ equals