Angular Frequency in Magnetic field

May 2009
4
0
Q. Two identical particles moving with the same speed enter a region of uniform magnetic field. If one enters normal to the direction of the field and the other enters at an angle 30° to it, find the ratio of their angular frequencies.

My attempt :
F1 = qvB sin90 = qvB
F2 = qvB sin30 = qvB/2

ω = qB/m
I can't seem to proceed further. How do I relate the forces to their frequencies?
 
Last edited:

Parvez

PHF Hall of Honor
Feb 2009
365
182
India
For the first case you have qvB = mv^2/r => qB=mv/r and putting v =rw you get w = qB/m ( w stands for omega ). Note this angular frequency does not depend upon the speed of the charged particle.

In second case particle enters making an angle 30 degree with B. Resolve this velocity in to rectangular components. vcos30 along the field and vsin30 perpendicular to the field. vcos30 will cause a translatory motion of the particle along the magnetic field and vsin30, being perpendicular to B will cause the particle to move in the circle. Hence the particle will follow a helical path. Since angular frequency does not depend upon the velocity, it will remain same as that of the first case. The ratio is obviously 1:1