Question

An electron is accelerated from rest by an electric field. After the acceleration, the electron is injected into a uniform magnetic field of 1.27 times 10-3 T. The velocity of the electron and the magnetic field lines are perpendicular to one another. The electron remains in the magnetic field for 5.13 times 10-9 seconds. The angle (in radians) between the initial electron velocity and the final electron velocity is ____.

Answer 1

Answer:

Explanation: the electron will move uniformly in circular path in magnetic field .

Let B be magnetic field , r be radius of circular path , v and ω be linear and angular velocity of electron , q and m  be charge on electron and mass of electron

centripetal force = magnetic force on electron

mω²r = B q v

mω² = B q (v / r)

mω² = B q ω

ω = B ( q / m )

= 1.27 x 10⁻³ x( 1.6 x 10⁻¹⁹ / 9.1 x 10⁻³¹ )

= .2233 x 10⁹ rad / s

angle of rotation by electrons

= angular velocity x time

= .2233 x 10⁹ x 5.13 x 10⁻⁹

= 1.145 radian .