Two identical charged particles moving with the same speed enter a region of uniform magnetic field. If one of these enters normal to the field direction, and the other enters at an angle of 30 degrees with the field, what would be the ratio of their angular frequencies?
Lorentz force on the charged particle = qvBsin(theta) where theta is the angle between v and B.
Centripetal force on the particle as it moves along a circular path = mv^2/r
The Attempt at a Solution
Equating the above two equations we get
v=qBr / msin(theta)
Therefore w(omega)=qB/msin(theta) (since v=rw)
On the above basis the ratio of the angular frequencies is 1:2 (since theta is 90 deg. in one case, and 30 deg. in the other case).
Since the answer as quoted in books is 1:1, I am unable to find out where I have gone wrong. Would appreciate some tips in case my method is not correct. Thanks.