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Q.

A charged particle of specific charge qm=α is released from origin at time t=0 with velocity V¯=V0i^+j^ in uniform magnetic field  B¯=B0i^. Co-ordinates of the particle at time t=πB0α  are.

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a

v02B0α,2.v0αB0,−v0B0α

b

−v02B0α,0,0

c

0,2v0B0α,v0π2B0α

d

v0πB0α,0,−2v0B0α

answer is D.

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Detailed Solution

α=qm, Path of the particle will be a helix of time period T=2πmBoq=2πB0α  The given time  t=πB0α=T2∴ Coordinates of particle at time  t=T2Would be  VxT/2,0,−2rHere,  r=mV0B0q=v0B0α ∴The coordinates are VoπB0α,0,−2V0Boα .
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A charged particle of specific charge qm=α is released from origin at time t=0 with velocity V¯=V0i^+j^ in uniform magnetic field  B¯=B0i^. Co-ordinates of the particle at time t=πB0α  are.