Correct Option: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Step 1 (Governing Law & Definition): [0.25 Mark]

The magnetic force $\vec{F}_m$ acting on a charged particle $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force law:

$$\vec{F}_m = q(\vec{v} \times \vec{B})$$

Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]

The work done $W$ by the magnetic force on the charged particle over a small displacement $d\vec{l}$ is given by:

$$dW = \vec{F}_m \cdot d\vec{l} = \vec{F}_m \cdot (\vec{v} dt)$$

Substituting the expression for $\vec{F}_m$:

$$dW = [q(\vec{v} \times \vec{B})] \cdot \vec{v} dt$$

Since the cross product $(\vec{v} \times \vec{B})$ is always perpendicular to $\vec{v}$, the dot product of the force and velocity is zero:

$$(\vec{v} \times \vec{B}) \cdot \vec{v} = 0$$

Therefore, $dW = 0$. By the Work-Energy Theorem, the change in kinetic energy $\Delta K = W = 0$.

Step 3 (Final Concluded Answer): [0.25 Mark]

Since the work done by the magnetic force is zero, the kinetic energy (and thus the total energy) of the charged particle remains constant. Hence, Assertion (A) is true, and Reason (R) correctly explains it.

💡 EL10 Concept Insight: Think of the magnetic force like a steering wheel in a car; it can change the direction you are moving, but it doesn't push the gas pedal, so your speed (and energy) stays exactly the same.