A uniform magnetic field Bis set up along the positive X-axis

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movingcharges

#1

A uniform magnetic field Bis set up along the positive X-axis. A particle of charge q and mass m moving with a velocity v enters the field at the origin in XY-plane such that it has velocity components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation.


#2

The path of the charged particle will be helix. As, the charge moves linearly in the direction of the magnetic field with velocity v cosθ and also describe the circular path due to velocity v sin θ.
Time taken by the charge to complete one circular rotation,