Final answer:
The magnitude of the magnetic induction B required is given by a) B = mv/qR, ensuring that the particle follows a circular path and hits the target, derived from equating the magnetic force to the centripetal force needed for circular motion. Option A is correct.
Step-by-step explanation:
The question involves finding the magnitude of magnetic induction (magnetic field strength, B) required to ensure a particle with a known mass (m), velocity (v), charge (q), and trajectory with radius (R) hits a target when moving in a magnetic field.
Using the Lorentz force equation F = qvB sin 0, where F is the force experienced by a charge, we can solve for B when the charge moves perpendicular to the magnetic field, making the angle (0) between the velocity and the magnetic field 90 degrees and sin 0 equals 1.
To make the charged particle hit the target, it must move in a circular path due to the magnetic force acting as the centripetal force. Here, the correct formula to find the magnetic field strength (B) is B = mv/qR which ensures the particle's circular motion with radius R.
Therefore, the correct answer is a) B = mv/qR. The centripetal force keeping the particle in a circular path is provided by the magnetic force (qvB), and setting this equal to the centripetal force (mv2/R) gives us the formula for the magnetic field strength required.