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 36.4 km/s enters a uniform, vertical, 1.18 T magnetic field.

Part A

What is the diameter of the path followed by this alpha particle? answer is in mm

Express your answer in millimeters to three significant figures.

Part B

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

Answer with an explanation. Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Part C

What is the magnitude of the acceleration of the alpha particle while it is in the magnetic field? answer is in m/s^2

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

Part D

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

Answer with an short explanation. Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Explanation / Answer

A). F = qvB = mv^2/R
R = mv/(qB)
diameter D = 2R = 6.64*10^-27*36400/(1.602*10^-19*1.18) = 1.28*10^(-3) m = 1.28 mm

B) The direction of this force will be tangential to the velocity vector because of the cross product (the result of the cross product is mutually orthogonal to the vectors v and B ). So the force will only act to change the direction of the particle's velocity.

C). F = ma
a = mv^2/R = 2*36400^2/1.28*10^(-3) = 2.07*10^12 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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