A particle of mass m and q has an initial velocity v→=v0j^ . If an electric field  E→=E0i^ and magnetic field   B→=B0i^act on the particle, its speed will double after a time:

Since, B→ is perpendicular to initial velocity, magnitude of velocity does not change in y−z plane.​⇒vo2=vy2+vz2and E→ can accelerate particle only along x axis.​⇒ax=qE0mAt any given time speed of particle is , v=vx2+vy2+vz2​When speed becomes double, we can write 2vo=vx2+vy2+vz2​⇒2vo=vx2+vo2⇒vx=3vo Using equation of kinematics, ​vx=ux+axt​⇒3v0=0+qE0mt​⇒t=3mv0qE0