Question

An electron enters with a velocity `vecv=v_0hati` 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 x-y plane. Suggest a configuration of fields `vecE` and `vecB` that can lead to it.

Answer 1

Considering magnetic field `B=B_(0)hatk`, and an electron enters with a velocity `v=v_(0)hati` and `a` cubical region (Faces parallel to coordinate planes.)
The force on electron, using magnetic lorentz force, is given by
`F=-e(v_(0)hatixxB_(0)hatk)=ev_(0)B_(0)hati`
Which revolves the electron in x-y plane.
The electric force `F=-eE_(0)hatK` accelerates e along z-axis which in turn encreases the radius of circuclar path and hence particle traversed on spiral path.