Question

The path of an electron in a uniform magnetic field may be

• A. circular but not helical
• B. helical but not circular
• C. neither helical nor circular
• D. either helical or circular

Answer 1

Answer: (D)

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.