A positively charged particle is projected parallel to a nearby current-carrying long conductor in the direction of current. The charged particle
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → will be attracted to the conductor.
The long conductor produces a magnetic field that circles it, and a moving charge feels the magnetic force \( \vec{F} = q\vec{v}\times\vec{B} \). A positive charge moving in the direction of the current behaves like a parallel current, and parallel currents attract.
Take the wire along the x-axis with the current in the \( +x \) direction and the particle on the \( +y \) side, moving along \( +x \). By the right-hand rule the field of the wire at the particle is along \( +z \).
\( \vec{v} = v\hat{\imath} \)
\( \vec{B} = B\hat{k} \)
\( \vec{F} = qvB\,(\hat{\imath}\times\hat{k}) = -qvB\,\hat{\jmath} \)
The force is along \( -\hat{\jmath} \), from the particle towards the wire, so the particle is attracted to the conductor.
Why the other options are incorrect
Option (1) will follow circular path around conductor. — Incorrect. The force is perpendicular to the circular field lines, so the particle does not follow them.
Option (2) will be repelled and deflected away from the conductor. — Incorrect. A particle moving opposite to the current would be repelled (antiparallel currents repel).
Option (4) will go undeflected in straight line — Incorrect. Here \( \vec{B} \) is perpendicular to the velocity, so there is a sideways force.