Question

Suppose a proton moves to the right and enters a uniform magnetic field into the page. It follows trajectory B with radius rp. An alpha particle (twice the charge and 4 times the mass) enters the same magnetic field in the same way and with the same velocity as the proton. Which path best represents the alpha particle’s trajectory?

Answer 1

R = r_protón / 2

Step-by-step explanation:

The alpha particle when entering the magnetic field experiences a force and with Newton's second law we can describe its movement

F = m a

Since the magnetic force is perpendicular, the acceleration is centripetal.

a = v² / R

the magnetic force is

F = q v x B = q v B sin θ

the field and the speed are perpendicular so the sin 90 = 1

we substitute

qv B = m v² / R

R = q v B / m v²

in the exercise they indicate

the charge q = 2 e

the mass m = 4 m_protón

R = 2e v B / 4m_protón v²

we refer the result to the movement of the proton

R = (e v B / m_proton) 1/2

the data in parentheses correspond to the radius of the proton's orbit

R = r_protón / 2