A particle of charge q and mass m starts moving from the origin under the action of an electric field E=Eoi^  and  B=Boi^ with velocity  V→=Voj^. The speed of the particle will become 2V0 after a time

Given, E=Eoi^ , B=Boi^ and V=Voj^ ∴ V→ ⊥ E→  and V→ ⊥ B→ Hence, the path is helix with speed remaining constant for the circular path in the YZ plane and uniform accelerated motion ax=Eqm along x axis. ∴Vy2+Vz2=Vo2 .............(1) Now at any given time speed is given by,  V=Vx2+Vy2+Vz2 ⇒ V2=Vx2+Vo2     [using (1)]Given, V=2V0; and here Vx=axt 4Vo2=axt2+Vo2 ⇒axt2=3Vo2 ⇒t=3Voax=3VomEq              ∵ ax=Eqm