Answer to Question #282993 in Mechanics | Relativity for BIGIRIMANA Elie

Question

An electron traveling at relativistic speed moves perpendicular to a magnetic field of 0.20 𝑇. Its path is circular, with a radius of 15 𝑚. Find: (a) the momentum, (b) the speed, and (c) the kinetic energy of the electron. Recall that, in nonrelativistic situations, the magnetic force 𝑞𝑣𝐵 furnishes the centripetal force 𝑚𝑣 2⁄𝑟. Thus, since 𝑝 = 𝑚𝑣 it follows that 𝑝 = 𝑞𝐵𝑟 and this relation holds even when relativistic effects are important. 

Answer 1

a)

$qvB=\frac{mv^2}r,$

$qB=\frac{mv}r,$

$p=qBr=4.8\cdot 10^{-19}~\frac{kg\cdot m}s,$

b)

$v=\frac pm=5.3\cdot 10^{11}~\frac ms,$

c)

$E=\frac {mv^2}2=2.5\cdot 10^{-9}~J.$