Question Analysis: Assertion-Reason type question (1 Mark).
Step 1 (Governing Law & Analysis of Assertion): [0.5 Mark]
The magnetic force on a charged particle is given by the Lorentz force formula:
$$\vec{F} = q(\vec{v} \times \vec{B})$$For a particle moving in the x-y plane with velocity $\vec{v} = v\cos\theta \hat{i} + v\sin\theta \hat{j}$ and a magnetic field $\vec{B} = B\hat{j}$, the force is:
$$\vec{F} = q[(v\cos\theta \hat{i} + v\sin\theta \hat{j}) \times B\hat{j}] = qvB\cos\theta (\hat{i} \times \hat{j}) = qvB\cos\theta \hat{k}$$Since the force is perpendicular to the velocity and the magnetic field, and the velocity component parallel to the field ($v\sin\theta$) remains constant, the particle moves in a helical path with its axis parallel to the y-axis (the direction of $\vec{B}$), not the x-axis. Thus, the Assertion (A) is False.
Step 2 (Analysis of Reason): [0.5 Mark]
The magnetic force $\vec{F} = q(\vec{v} \times \vec{B})$ is always perpendicular to both the velocity vector $\vec{v}$ and the magnetic field vector $\vec{B}$ by the definition of the cross product. Therefore, the force cannot be along the velocity of the particle. Thus, the Reason (R) is False.
Step 3 (Final Concluded Answer): [1 Mark]
Correct Option: (d) Both Assertion (A) and Reason (R) are false statements.
💡 EL10 Concept Insight:
Think of the magnetic force like a steering wheel that only pushes sideways—it can never push you in the direction you are already traveling, which is why the force is always perpendicular to your velocity. Also, a charged particle always spirals around the magnetic field lines like a bead sliding along a wire, so the axis of the spiral must follow the magnetic field, not the x-axis!