Question

A particle of mass $m$ and charge $q$ with an initial velocity $v$ is subjected to a uniform magnetic field $B$ along the vertical direction. The particle will

• A. follow a circular path if v is along the vertical direction
• B. make helical motion if v is along the horizontal direction
• C. make helical motion if v is neither parallel nor orthogonal to B
• D. always make circular motion

Answer 1

Answer: (C)

make helical motion if v is neither parallel nor orthogonal to B

Answer 2

When a charged particle $q$ move with velocity $v$ inside a uniform magnetic field $B$, then force acting on it.
$F =q( v \times B )=2 q\,v B\,\sin \theta$
Since we know that, if $v$ and $B$ are neither orthogonal nor parallel i.e., $\theta \neq 0,90^{\circ}$ and $180^{\circ}$ then particle will describe a helical motion.
However, if $v$ and $B$ are perpendicular to each other, then particle will describe a circle.