An electron enters with a velocity v = v 0 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 x-y plane. Suggest a configuration of fields E and B that can lead to it.

Question

Philoid · Accepted Answer

The velocity of the particle is v₀i. So, to construct a spiral motion we need to increase radius gradually. As magnetic field cannot do work the electric filed should increase the radius. Hence, E=E₀i.

To balance the force in x direction and to make a spiral motion we need a force in y direction. Again,

To get force in y direction B must be in the z direction. i.e. B=B₀k.