Q.

A particle of charge q and mass m starts moving from the origin under the action of an electric field E→=E0i^ and B→=B0i^ with a velocity v→=v0j^. The speed of the particle will become 2v0 after a time

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a

t=2mv0qE

b

t=2Bqmv0

c

t=3Bqmv0

d

t=3mv0qE

answer is D.

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Detailed Solution

E→ is parallel to B→ and v→ is perpendicular to both. Therefore, path of the particle is a helix with increasing pitch. Speed of particle at any time t isv=vx2+vy2+vz2   ……..(i)Here, vy2+vz2=v02and    v=2v0⇒vx=3v0           vx=axt⇒3v0=qEmt⇒t=3mv0qE
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