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: Physics
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?

Physics

Alan Giambattista,… 2nd Edition

Chapter 16, Problem 52

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Solved by Expert Zulfiqar Ali

05/27/2020

Step 1

The electric force is given by $F_{e}=qE$, where $q=1.60 \times 10^{-19} \, \text{C}$ is the charge of the proton and $E=6.5 \times 10^{3} \, \text{N/C}$ is the electric field. This gives us $F_{e}=1.04 \times 10^{-15} \, \text{N}$. The gravitational force is 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

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.

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.

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