Dennis O. answered • 11/26/23
Tutoring nursing, physiology, anatomy, Biology, and DNP Projects.
a) To find the magnitude of the maximum magnetic force exerted on the proton, we can use the formula for the magnetic force on a charged particle moving through a magnetic field:
\[ F = qvB \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( v \) is the velocity of the particle, and
- \( B \) is the magnetic field strength.
In this case, the charge of a proton is \( q = 1.6 \times 10^{-19} \, \mathrm{C} \), the velocity is \( v = 6.00 \times 10^5 \, \mathrm{m/s} \), and the magnetic field strength is \( B = 1.50 \, \mathrm{T} \).
Substituting these values into the formula, we get:
\[ F = (1.6 \times 10^{-19} \, \mathrm{C}) \times (6.00 \times 10^5 \, \mathrm{m/s}) \times (1.50 \, \mathrm{T}) \]
Calculating this expression, we find:
\[ F = 1.44 \times 10^{-13} \, \mathrm{N} \]
Therefore, the magnitude of the maximum magnetic force exerted on the proton is \( 1.44 \times 10^{-13} \, \mathrm{N} \).
(b) To find the magnitude of the maximum acceleration, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
\[ F = ma \]
In this case, the force is the magnetic force we calculated in part (a), and the mass of a proton is approximately \( 1.67 \times 10^{-27} \, \mathrm{kg} \). Therefore, we have:
\[ 1.44 \times 10^{-13} \, \mathrm{N} = (1.67 \times 10^{-27} \, \mathrm{kg}) \times a \]
Solving for \( a \), we find:
\[ a = \frac{1.44 \times 10^{-13} \, \mathrm{N}}{1.67 \times 10^{-27} \, \mathrm{kg}} \]
Calculating this expression, we get:
\[ a \approx 8.63 \times 10^{13} \, \mathrm{m/s^2} \]
Therefore, the magnitude of the maximum acceleration is approximately \( 8.63 \times 10^{13} \, \mathrm{m/s^2} \).
No, the field would not exert the same magnetic force on an electron moving through the field with the same speed. The magnetic force experienced by a charged particle moving through a magnetic field depends on the charge of the particle. Since the charge of an electron is opposite in sign to that of a proton, the force experienced by an electron would be in the opposite direction. Therefore, the magnitude of the magnetic force on an electron moving through the field with the same speed would be the same as that on the proton, but the direction would be opposite.
