Answer to Question #146073 in Physics for Khan Asf

Question

An alpha particle travelling at the velocity of 100 km/s flies at an angle 20° into a 1 meter wide area of homogeneous magnetic field with induction 5 mT as shown in the figure. The velocity direction of alpha particle is perpendicular to the field induction lines. In what time will the alpha particle leave the homogeneous magnetic field? Neglect the gravity action. Take the alpha particle charge-to mass ratio as 4.8 x (10)^7 C/kg. Give your answer in microseconds and round it to the whole.

Answer 1

Under the influence of magnetic field, the particle will experience a force that will bend its trajectory from a straight line. However, we can neglect this since at 1 m gap the trajectory can be assumed straight.

The magnetic force is

$$F=qvB\text{ sin}\alpha.$$

The acceleration is

$$a=F/m=\frac{qvB\text{ sin}\alpha}{m}.$$

The speed after 1 m of acceleration:

$$v_f=\sqrt{v_i^2+2ad}=\sqrt{v_i^2+\frac{2dqvB\text{ sin}\alpha}{m}}.$$

The time it will take is

$$t=\frac{\Delta v}{a}=\frac{v_f-v_i}{a},\\\space\\ t=8\space\mu\text{s}$$