In a cyclotron, a charged particle
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → undergoes acceleration all the time
Acceleration is the rate of change of the velocity vector, so it exists whenever the speed or the direction changes.
Inside a dee there is no electric field, only the magnetic field. The magnetic force is perpendicular to the velocity, so it changes the direction but not the speed. The particle moves on a semicircle and has the centripetal acceleration
\( \displaystyle a = \frac{v^{2}}{r} = \frac{qvB}{m} \)
In the gap between the dees the oscillating electric field points along the motion, so the particle gains speed and is again accelerated. It is therefore accelerated at all times.
Why the other options are incorrect
Option (1) slows down within a dee and speeds up between dees — Incorrect. The speed stays constant inside a dee; the particle never slows down.
Option (3) speeds up between the dees because of the magnetic field — Incorrect. A magnetic force does no work; the electric field in the gap speeds the particle up.
Option (4) speeds up in a dee — Incorrect. The dees shield the interior from the electric field, so there is nothing to increase the speed there.
Note: A similar question was also asked in CUET (UG) 2023 on 13-06-2023 (Slot 3) and on 11-06-2023 (Slot 3).
NCERT Exemplar:
Moving Charges and Magnetism – …
