1) In a region of space a uniform magnetic field  B is along a positive x - axis. Electrons are emitted from the origin with speed v at different angles. Show that the paraxial electrons are focussed on the x - axis at a distance  2 pie m v / Be. Here m is the mass of the electron and e is the charge on it.

2) A particle of mass m and charge q is lying at the origin in a niform magnetic field B directed along the x-axis. A time t=0, it is a given velocity v0 at an angle @ with the y-axis in the x-y plane. Find the coordinates of the particle after one revolution

 2

the component of velocity if particle along y axis is V cos @

due to this component particle will move in circle in y-z plane.

and due to x component particle will be in translatory motion wid constant velocity  = Vsin @

initially particle was at origin hence it will come back to origin in one time peirod.

hence its y and z co -ordinate will be ( 0,0)

but it will travel some distance in x direction in that time interval

distance travel in x direction  =  T * v sin@       ( T = 2 pie m / q B)

hence its co - ordinate after one complete revolution is

( 2 pie m vsin@ / qB , 0 ,0)