A charged particle is introduced at the origin x = 0 , y = 0 , z = 0 with a given initial velocity v → . A uniform electric field E → and a uniform magnetic field B → exist everywhere. The velocity v → , electric field E → and a uniform magnetic field B → are given in the columns below Column 1 Column 2 Column 3 1. Electron with v → = 2 E 0 B 0 x ^ (i) E → = E 0 z ^ (P) B → = - B 0 x ^ 2. Electron with v → = E 0 B 0

Step-by-step solution

Given: A charged particle is introduced at the origin ((x=0, y=0, z=0) ). initial velocity (= v ), uniform electric field ( E ). uniform magnetic field ( B ). Also the values are given the table. we need to find the cases where the particle will move in a straight line with constant velocity. To move a particle with constant velocity; Fnet (=0 ), ( ) The electric force (= ) magnetic fore e. ( gathered q E=q v B . E=v B . gathered ) Now checking the options. ( aligned & A) (II) (iii) (s). & (II) = v = E₀ B₀ y . & (i