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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:

a
3mv0qE0
b
2mv0qE0
c
3mv0qE0
d
2mv0qE0

detailed solution

Correct option is A

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

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