5th December 2008

we will just take two velocities
one perpendicular to the magnetic field
and one along it

the one along it will not change its direction as well magnitude

but the one perpendicular to it will make a circular path (i mean to say that velocity )

if we look from the rear view the path will be a circle

so at any point of time x distance= v_xt

y distance =∫v_psinθdt
but dθ/dt=w =constant (as velocity perpendicular is constant)

so y distance ₀∫^tv_psinwtdt = (v/w)(1-coswt)

and z distance = ₀∫^tv_pcoswtdt

=(v_p/w)sinwt

see the velocity along the field will not change its magnitude as well as direction as
the force =qv*B= qvBsinθ = 0 (as theta = 0)

and the velocity perpendicular to the magnetic field will have a froce always towards its centre
(the old case of cyclotron)
and this magnitude will be constant as B doesnt do any work on the system!!

here only w is needed

and v is vy(v perpendicular) in this case

for w

mv²/r=qvB

so v/r=qvB/mv = w

for the mathematical derivation

we see that ifthe body has rotated to an angle θ from vertical

then its velocity makes an angle of 90- θ with the vertical

so dy/dt=v_psinθ and the result follows
similary for z

plz report if some loopholes are still left

i will be covering all of them