Alpha particles,each having a charge of +2e and a mass of 6.64 ×10^-27 kg,are accelerated in a uniform 0.80-T magnetic field to a final orbit radius of 0.30 m.The $\vec { B }$ field is perpendicular to the velocity of the particles.How long does it take an alpha particle to make one complete circle in the final orbit? (e = 1.60 × 10^-19C)

Question

Quizplus · Accepted Answer

The time period $T$ for a charged particle in a magnetic field is given by $T = \frac{2\pi m}{qB}$, where $m$ is the mass of the particle, $q$ is the charge, and $B$ is the magnetic field strength. For an alpha particle with a mass of $6.64 \times 10^{-27}$ kg and a charge of $+2e$ (where $e = 1.60 \times 10^{-19}$ C), in a $0.80$-T magnetic field, the time to complete one circle is calculated as follows:$$T = \frac{2\pi (6.64 \times 10^{-27})}{(2 \times 1.60 \times 10^{-19}) \times 0.80} = 1.5 \times 10^{-7} \text{ s} = 0.15 \, \mu\text{s}$$

Alpha Particles,each Having a Charge of +2e and a Mass B⃗\vec { B }B

Alpha Particles,each Having a Charge of +2e and a Mass $\vec { B }$