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 6.64×1027 kg ) traveling horizontally at 34.8 km/s enters a uniform, vertical, 1.00 T magnetic field.

A) What is the diameter of the path followed by this alpha particle?

Express your answer in millimeters to three significant figures.

B) What effect does the magnetic field have on the speed of the particle?

C) What is the magnitude of the acceleration of the alpha particle while it is in the magnetic field?

Express your answer in meters per second to three significant figures.

D) What is the direction of the acceleration of the alpha particle while it is in the magnetic field?

E) 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)

= 2*6.64*10^-27*34800/2*1.6*10^-19*1.00

= 1.44*10^(-3) m = 1.44 mm

b) has no effect on speed because Force magnetic and v are at right angles.

c). F = ma
a = mv²/R = 2mv²/D = 1.11*10^14 m/s²

d) 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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