A charged particle with charge `q` enters a region of constant, uniform and mututally orthogonal fields `vec(E) and vec(B)` with a velocity `vec(v)` perpendicular to both `vec(E) and vec(B)`, and comes out without any change in magnitude or direction of `vec(v)`. Then

Options

A. `vecV=(vecB xx vecE)/B^(2)`
B. `vecV=(vecE xx vecB)/E^(2)`
C. `vecV=(vecB xx vecE)/E^(2)`
D. `vecV=(vecE xx vecB)/B^(2)`

Answer

D

Explanation

Force on the charged particle due to electric field`=qvecE` and force on the charged particle due to magnetic field `=q(vecV xx vecB)` Since the particle comes out without any devianation, the two forces must be equal and opposite As the net force is zero `qE=BqV therefore V=E/B=(EB)/B^(2)=(EBsin90)/B^(2) therefore vecV =(vecE xx vecB)/B^(2)`.