Question

Suppose that a region with a uniform magnetic field B also has a uniform electric field E perpendicular to the magnetic field, an arrangement called crossed fields. Show that for a charged particle moving in such crossed fields in a direction perpendicular to both E and B, the electric force cancels the magnetic force, provided the particle has a speed

v= E/B

If the magnetic field is in the vertical upward direction and the electric field is in the northward direction, what must be the direction of motion of the charged particle to produce this cancellation? Crossed fields are used in velocity selectors, or velocity filters. In these devices, a beam of charged particles if aimed into a region of crossed fields, and this deflects particles out of the beam, except for those particles that have the critical velocity v = E/B

Please show your work!

Answer 1