First slide

Force on a charged particle moving in a magnetic field

Question

A charged particle is moving in a circular path in a magnetic field. A resistive force starts acting on the particle whose direction is opposite to the direction of its motion and magnitude is directly proportional to its velocity. Now the particle starts moving in a spiral path, then

Difficult

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.

Solution

Radius r of particle in spiral path at any time when velocity is v
$r = \frac{mv}{qB}; ω = \frac{v}{r} = \frac{qB}{m} \Rightarrow constant$
Angular momentum $L = mvr = {qBr}^{2}$ 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 force on the particle = kv, where k is a constant As velocity decreases so net force acting on the particle will decrease.

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