Question

Several protons of different speeds enter a uniform magnetic field confined in a cylindrical region. Each proton enters field radially, then choose correct options about time interval spent by them in magnetic field.

• A. Faster is particle, lesser is time
• B. Faster is particle, greater is time
• C. Slower is particle, greater is time
• D. Time is independent of speed

Answer 1

Answer: (A), (C)

The correct options are
A Faster is particle, lesser is time
C Slower is particle, greater is time

Time taken = $\frac{\text{distance}}{\text{speed}}$ = $\frac{r\theta }{v}$
$r=\frac{mv}{qB}$
Therefore, time taken = $\frac{m\theta }{qB}\propto \theta$
From the diagram,
$\tan \frac{\theta }{2}=\frac{R}{r}=\frac{RqB}{mv}$
If $v$ increases, $\theta$ decreases, so time also decreases.