Question

A charged particle is moving in a circular path in a magnetic field. Aresistive force starts acting on the particle whose direction is oppositely directed to its motion and magnitude is directly proportional to its velocity. Now the particle starts moving in a spiral path; then

• A. Angular velocity of the particle decreases continuously.
• B. Angular momentum of the particle remains constant.
• C. Magnetic field is lying only perpendicular to the plane of coil.
• D. Net force acting on the particle remains constant.

Answer 1

Answer: (C)

Radius $R$ of particle in spiral path at any time when velocity is $v$.
$r=\frac{mv}{qB}\omega =\frac{v}{r}=\frac{qB}{m}\to$ constant
Angular momentum, $L=mvr=qB{r}^2\to$ decreases as $r$ decreases
If particle is moving in a plane then its velocity and acceleration will be in that plane. The force on the particle will also be in that plane. It means magnetic field should be perpendicular to that plane.
Magnetic force on the particle $=qvB$
Resistive on the particle $=kv$, where $k$ is a constant
As velocity decreases, so net force acting on the particle will decrease.