An alpha particle (a He nucleus, containing two protons and two neutrons and hav

Question

An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of 6.64 Times 10^-27 kg) traveling horizontally at 35.6 km/s enters a uniform, vertical. 1.10-T magnetic field. (a) What is the diameter of the path followed by this alpha particle? (b) What effect does the magnetic field have on the speed of the particle? (c) What are the magnitude and direction of the acceleration of the alpha particle while it is in the magnetic field? (d) Explain why the speed of the particle does not change even though an unbalanced external force acts on it?

Explanation / Answer

a)

F = qvB = mv²/R
R = mv/(qB)
diameter D = 2R = 2mv/(qB) = 1.34*10^(-3) m = 1.34 mm

where m = 6.64 x 10^-27 kg

q = 2e

B = 1.10 T

v = 35.6 km/s = 36600 m/s

b)

F = ma
a = mv²/R = 2mv²/D = 1.89*10^12 m/s²

c)

direction of acceleration is toward to the center, perpendicular to the velocity. It only changes the direction of velocity and doesn't change its speed.

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