Solution for Question 13
Analysis: The particle is subjected to two forces:
- Viscous Drag Force: $\vec{f} = -b\vec{v}$. This force opposes motion and continuously reduces the speed (magnitude of velocity).
- Magnetic Force: $\vec{F}_m = q(\vec{v} \times \vec{B})$. This force is always perpendicular to velocity. It changes the direction of motion but does not change the speed.
Because the drag force constantly reduces the speed $v$, and the radius of curvature in a magnetic field is given by $R = \frac{mv}{qB}$, the radius $R$ is directly proportional to $v$.
As $v$ decreases, $R$ decreases. A path with a continuously decreasing radius of curvature is a spiral.
Correct Answer: (c)
spiralling into a point.