Question

A particle of mass $m$ and charge $q,$ moving with velocity $V$ enters Region $II$ normal to the boundary as shown in the figure. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region $II$ is $\ell$ Choose the correct choice(s).

• A. The particle enters Region III only if its velocity $V>\frac{q\ell B}{m}$
• B. The particle enters Region III only if its velocity $V<\frac{q\ell B}{m}$
• C. Path length of the particle in Region II is maximum when velocity $V=\frac{q\ell B}{m}$
• D. Time spent in Region II is same for any velocity V as long as the particle returns to Region I

Answer 1

Answer: (A), (C), (D)

The particle enters Region III only if its velocity $V>\frac{q\ell B}{m}$
Path length of the particle in Region II is maximum when velocity $V=\frac{q\ell B}{m}$
Time spent in Region II is same for any velocity V as long as the particle returns to Region I

Path of the particle in region II is circular.
If the width $l$ of region $II$ is less than the radius$(r=\frac{mv}{qB})$ of the circle, the particle will enter region C( i.e $l<\frac{mv}{qB}$ i.e $v>\frac{qlB}{m}$ )
If $v=\frac{qlB}{m}$, particle will have max path length in region $II$.
If the particle returns to region $I,$ time spent inside region II is $\frac{1}{2}$ of $T=\frac{2\pi m}{qB}$ which is independent of $v$.