JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Magnetic Effects of Current

The particle moves in a circular arc with radius $r=\frac{mV}{qB}$. For the particle to enter Region III, it must traverse the width $\ell$, requiring $r>\ell$, i.e., $V>\frac{q\ell B}{m}$ (A is correct). The path length is maximum when the particle just grazes the boundary, i.e., when $r=\ell$ or $V=\frac{q\ell B}{m}$ (C is correct). The time spent in Region II for a particle returning to Region I depends only on the angle subtended, which is determined by the geometry, making the time constant for particles that return (D is correct).