Question

A particle of mass m and charge q, moving with velocity v enters region II normal to the boundary as shown in the following figure. Region II has a uniform magnetic field B. Choose the correct choice(s).

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

Answer 1

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

The correct options are
A

The particle enters region III only if its velocity v > $\frac{qIB}{m}$

C

Path length of the particle in region II is maximum when velocity v = $\frac{qIB}{m}$

D

Time spent in region II is same for any velocity v as long as the particle returns to the region I.

i.e., $\frac{mv}{qB}$ > I or v > $\frac{qlB}{m}$

So, (a) is correct and (b) is wrong. It is clear from the diagram that path length of particle in region II is maximum when $R=\frac{mv}{qB}=1$

So, $v=\frac{qlB}{m}$ for maximum path length in region II.

If the particle has to return to region I, then time spend by particle in region II is $\frac{T}{2}$

i.e., t = $\frac{\pi m}{qB}$ which is independent of v, therefore (d) is correct.