Problem 2: A particle with cha
Problem 2: A particle with charge q is emitted from the originwith momentum p directed at an angle ? to a uniform magnetic fieldB which lies in the z-direction. i) What is the position of theparticle as a function of time? ii) At what point does the particlenext intersect the z-axis?
Answer:
At time t = 0, the charge is at the origin with aninitial velocity, 
The equation of motion for the particle of mass m andcharge q in a uniform magnetic field in thez-direction is
The equation of the motion in x, y & z direction are asfollow:-
(b)
At t=0 particle is at origin.The particle crosses the z axis ifx(t)=0 and y(t)=0.
From the motion equation , we can see that x(t) = 0 when
with n as an integer. Similarly y(t) = 0 when 
where n’ is an different integer.
First time after t=0 both x(t) & y(t) become zero is whenn=2 and n’ =1.
Thus, 
. This is equivalent to one gyro-period.
Hence, at every time which is a multiple of the gyro-period, thecharged particles intersects the z-axis.
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