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.
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
