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Q.
The path of an electron in a uniform magnetic field may be
AFMCAFMC 2007
Solution:
When the angle between magnetic field $\vec{ B }$ and velocity vector $\vec{ v }$ is $90^{\circ}$, so the force will be maximum and always perpendicular to motion, so the path will be circular. When the electron is moving at an angle to the field (other than $0^{\circ}, 90^{\circ}$, or $180^{\circ}$ ), then electron moves with constant velocity $v \cos \theta$ along the field (as no force acts on a charged particle when it moves parallel to the field) and at the same time it is also moving with velocity $v \sin \theta$ perpendicular to the field due to which it will describe a circle (in a plane perpendicular to the field) of radius
$r=\frac{m(v \sin \theta)}{q_{B}}$
So, the resultant path will be a helix with its axis parallel to the field $\vec{ B }$ as shown in figure.
