Question

A particle of charge q and mass m enters normally (at point P) in a region of magnetic field with speed v. It comes out normally from Q after time T as shown in fig. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is/are correct?

• A. $B=\frac{mv}{qR}$
• B. $T=\frac{\pi R}{2v}$
• C. $T=\frac{\pi m}{2qB}$
• D. none of these

Answer 1

Answer: (A), (B), (C)

$B=\frac{mv}{qR}$
$T=\frac{\pi R}{2v}$
$T=\frac{\pi m}{2qB}$

The particle will move along an arc which is path of a circle of radius:

$r=\frac{mv}{Bq}$

From fig, we can see that $r=R$

$\therefore R=\frac{mv}{Bq}$

$T=\frac{\pi r/2}{v}=\frac{\pi r}{2v}=\frac{\pi R}{2v}(\because r=R=\frac{mv}{Bq})$

$\therefore T=\frac{\pi m}{2Bq}$