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magnetic force on particle = qvBsin@
when velocity is parallel to magnetic then @ = 0 or 180,
then magnetic force is qvBsin0 = 0
electric force is F = qE
net force = electric force+ magnetic force = qE
net force is electric force along the direction of motion...so the motion of charged particle is straight line acclerated motion...
As the charge is at rest, it will accelerate by elctric field along the line of electric field ( magnetic field only change direction of charge).
Now as the magnectic field is parallal to electric field, so charge will move along magnetic field.
From the forluma, Fm=qvBsinθ as the θ=0 Fm=0, hence no net force magnetic force acting on it (and hence it will not change its direction)
From above result, as only eletric force acting on it, charge particle will move in a straight line (along the line of electric field due to eletric force)