Solution:

Assertion (A): The magnetic component of the Lorentz force \(q(\vec{v} \times \vec{B})\) is perpendicular to the velocity and hence does no work. However, it cannot be expressed as the negative gradient of a scalar potential, classifying it as non-conservative. So, (A) is true.

Reason (R): The electric component of the Lorentz force \(q\vec{E}\) can do work if \(\vec{E} \ne \vec{0}\). Therefore, the work done by the total Lorentz force is not always zero. So, (R) is false. Thus, (A) is true but (R) is false.