Question

Consider the same situation as in Problem 51 , but with a proton entering through the small hole at the same angle with a speed of $v=8.50 \times 10^{5} \mathrm{~m} / \mathrm{s}$. (a) Can you ignore the force of gravity when solving this problem for the horizontal distance traveled by the proton? Why or why not? (b) How far will the proton travel, $\Delta x$, before it hits the metal plate?

Name: Problem 52, Chapter 16: College Physics With an Integrated Approach to Forces and Kinematics
Uploaded: 2020-05-27T15:26:10-08:00
Duration: 4 min 29 s
Channel: Zulfiqar Ali
Description: Consider the same situation as in Problem 51 , but with a proton entering through the small hole at the same angle with a speed of v=8.50 ×10^5 m / s. (a) Can you ignore the force of gravity when solving this problem for the horizontal distance traveled by the proton? Why or why not? (b) How far will the proton travel, Δx, before it hits the metal plate?

   Consider the same situation as in Problem 51 , but with a proton entering through the small hole at the same angle with a speed of $v=8.50 \times 10^{5} \mathrm{~m} / \mathrm{s}$. (a) Can you ignore the force of gravity when solving this problem for the horizontal distance traveled by the proton? Why or why not? (b) How far will the proton travel, $\Delta x$, before it hits the metal plate?

College Physics With an Integrated Approach to Forces and Kinematics

Alan Giambattista,… 3rd Edition

Chapter 16, Problem 52

Instant Answer

Solved by Expert Zulfiqar Ali

05/27/2020

Step 1

To assess whether we can ignore the force of gravity, we need to compare the gravitational force acting on the proton to the other forces involved, particularly the forces due to its motion. The gravitational force $ F_g $ acting on the proton can be Show more…

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Consider the same situation as in Problem 51 , but with a proton entering through the small hole at the same angle with a speed of $v=8.50 \times 10^{5} \mathrm{~m} / \mathrm{s}$. (a) Can you ignore the force of gravity when solving this problem for the horizontal distance traveled by the proton? Why or why not? (b) How far will the proton travel, $\Delta x$, before it hits the metal plate?

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Key Concepts

Lorentz Force

This is the force experienced by a charged particle moving in a magnetic field, given by F = q(v × B). It is responsible for the deflection of the particle and, in many practical scenarios with high speeds and strong magnetic fields, its magnitude greatly exceeds that of other forces like gravity.

Negligibility of Gravitational Force

In many charged particle applications, especially when the time of flight is very short and the electromagnetic forces are dominant, the gravitational force (mg) is so small in comparison that it can be ignored without significantly affecting the analysis of the horizontal motion.

Centripetal Motion in Magnetic Fields

When a charged particle is subjected to a magnetic field, the Lorentz force provides the necessary centripetal force that causes the particle to follow a circular or curved trajectory. Understanding how the magnetic force acts as a centripetal force is crucial for predicting the path of the particle.

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