Respuesta :
Answer:
Since proton is more massive than electron, thus its acceleration will be lesser in magnitude since acceleration is inversely proportional to acceleration.
However, its charge is opposite to that of electron. Thus it will experience the acceleration in the opposite direction.
Thus, the correct option is:
b) The resulting acceleration of the proton would be weaker in magnitude and oppositely directed compared to the acceleration of the electron.
Explanation:
The magnetic force and Newton's second law allow us to find the correct answer for the comparison of the acceleration of the proton and the electron is:
B) The resulting acceleration of the proton would be weaker in magnitude and oppositely directed compared to the acceleration of the electron.
given parameters
- Magnetic field in the + y direction is: [tex]B_y[/tex] = 6.34 T
- Electron velocity is: [tex]v_z[/tex] = 2.83 10⁶ m / s
- Magnetic force is: [tex]F_x[/tex] = 2.87 pn = 2.87 10-12 N
To find
- The acceleration if the electron is changed by a proton while maintaining the speed.
The magnetic force is a vector quantity given by the vector product of the velocity and the magnetic field.
[tex]F_m[/tex] = q v x B
Dodne [tex]F_m[/tex] is the magnetic force, q the charge, v the velocity and B the magnetic field.
Newton's second law establishes a relationship between the resultant force, the mass, and the acceleration of the body.
[tex]F_m[/tex] = m a
q v B sin θ = m a
a = qvB sin θ / m
The speed and the magnetic field are on different axes, so their angle is 90º and the sin 90 = 1
a = [tex]\frac{q \ v \ B}{m}[/tex]
The mass and charge of the proton are m = 1.67 10⁻²⁷ kg and q = 1.6 10⁻¹⁹C.
[tex]a_{protn} = \frac{1.6 \ 10^{-19} \ 2.83 \ 10^6 \ 6.34 }{1.37 \ 10^{-27} }[/tex]
[tex]a_{proton}[/tex] = 1,719 10¹⁵ m / s²
Let's find the acceleration of the electron that has mass m = 9.1 10⁻³¹ kg and charge q = -1.6 10⁻¹⁹ C.
[tex]a_{electron}=- \frac{1.6 \ 10^{-19} \ 2.83 \ 10^6 \ 6.34 }{9.1 \ 10^{-31} }[/tex]
[tex]a_{electron}[/tex] = - 3.27 10¹⁸ m / s²
We must make some observations between these two accelerations:
- The acceleration of the electron has a greater magnitude than the acceleration of the proton.
- The acceleration is centripetal in the two particles
- The acceleration of the electron and proton are in the opposite direction.
Let's analyze the claims:
A) False. The accelerations are in the opposite direction.
B) True. The acceleration of the proton is smaller and in the opposite direction, as shown above.
C) False. The acceleration of the proton is less than that of the electron.
D) False. The acceleration of the proton is less than that of the electron.
E) False. The acceleration of the proton is less than that of the electron.
F) False. The acceleration of the proton is less than that of the electron.
In conclusion they use the magnetic force and Newton's second law we can find the correct answer for the comparison of the acceleration of the proton and the electron is:
B) The resulting acceleration of the proton would be weaker in magnitude and oppositely directed compared to the acceleration of the electron.
Learn more here: brainly.com/question/9633443
