What is the magnetic force on a proton that is moving at [tex]$5.2 \times 10^7 m / s$[/tex] to the left through a magnetic field that is 2.4 T? Assume that the charge on a proton is [tex]$1.6 \times 10^{-19} C$[/tex]. Use [tex]$F = qvB$[/tex].
A. [tex]$2.0 \times 10^{-11} N$[/tex] down
B. [tex]$2.0 \times 10^{-11} N$[/tex] up
C. [tex]$8.3 \times 10^{-12} N$[/tex] down
D. [tex]$8.3 \times 10^{-12} N$[/tex] up
Answer (1)
Calculate the magnitude of the magnetic force using F = q v B : F = ( 1.6 \t × 1 0 − 19 C ) ( 5.2 \t × 1 0 7 m / s ) ( 2.4 T ) = 1.9968 \t × 1 0 − 11 N .
Determine the direction of the force using the right-hand rule: with the proton moving to the left and the magnetic field pointing into the page, the force is downwards.
Approximate the magnitude of the force to match the answer choices: 1.9968 \t × 1 0 − 11 N \t ≈ 2.0 \t × 1 0 − 11 N .
State the final answer: 2.0 \t × 1 0 − 11 N down
Explanation
Problem Analysis and Given Data We are given a proton moving through a magnetic field and asked to find the magnetic force on it. We are given the velocity of the proton v = 5.2 \t × 1 0 7 m / s , the magnetic field B = 2.4 T , and the charge of the proton q = 1.6 \t × 1 0 − 19 C . We will use the formula F = q v B to calculate the magnitude of the force and the right-hand rule to determine the direction.
Calculating the Magnitude of the Force First, we calculate the magnitude of the magnetic force using the formula F = q v B . Plugging in the given values, we have F = ( 1.6 \t × 1 0 − 19 C ) ( 5.2 \t × 1 0 7 m / s ) ( 2.4 T ) F = 1.9968 \t × 1 0 − 11 N So the magnitude of the force is approximately 2.0 \t × 1 0 − 11 N .
Determining the Direction of the Force Next, we need to determine the direction of the force. The proton is moving to the left, and the magnetic field is 'nemetins' (assuming this means into the page). Using the right-hand rule, we point our thumb in the direction of the velocity (left) and our fingers in the direction of the magnetic field (into the page). The palm of our hand then points in the direction of the force. In this case, the force is downwards.
Final Answer Therefore, the magnetic force on the proton is 2.0 \t × 1 0 − 11 N downwards.
Examples
The principles behind magnetic force calculations are crucial in designing and operating devices like MRI machines, which use strong magnetic fields to create detailed images of the human body. By understanding how charged particles interact with magnetic fields, engineers can optimize the performance of these machines, improving image quality and diagnostic capabilities. This same understanding is applied in particle accelerators, where magnetic fields guide and accelerate particles to incredibly high speeds for scientific research, enabling discoveries in physics and medicine.
