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 36.6 km/s enters a uniform, vertical, 1.10 T magnetic field.

Part A What is the diameter of the path followed by this alpha particle? Express your answer in millimeters to three significant figures.

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

Part 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.

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

Part E Explain why the speed of the particle does not change even though an unbalanced external force acts on it.

Explanation / Answer

a)

here by using the formula

F = q * v * B = m * v^2 / R

R = m * v / ( q * B)

diameter = D = 2 * R

D = 2 * m * v / (q * B)

D = (2 * 6.64 * 10^-27 * 36600) / ( 2 *1.602 * 10^-19 * 1.1) ..................(there is 2 proton so we multiply the charge by 2)

D = 1.379 * 10^-3 m

b)

B has no effect on speed because Force magnetic and v are at right angles

c)

F = m *a

a = v^2 /R

a = 2 * v^2 / D

a = ( 2 * 36600^2) / (1.379 * 10^-3)

a = 1.94 * 10^12 m/s^2

d)

the direction of acceleration is toward to the center perpendicular to the velocity

e)

it only changes the direction of velocity and doesnot change its speed

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