A proton is initially moving west at a speed of 1.05 x 106 m/s in a uniform magnetic field of magnitude 0.295 T directed vertically upward. Describe in detail the proton's trajectory, including its shape and orientation. the radius of the path the proton's trajectory --Select---
A proton is initially moving west at a speed of 1.05 x 106 m/s in a uniform magnetic field of magnitude 0.295 T directed vertically upward. Describe in detail the proton's trajectory, including its shape and orientation. the radius of the path the proton's trajectory --Select---
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Understanding Proton Trajectories in Uniform Magnetic Fields
**Problem Statement:**
A proton is initially moving west at a speed of \(1.05 \times 10^6 \, \text{m/s}\) in a uniform magnetic field of magnitude \(0.295 \, \text{T}\) directed vertically upward. Describe in detail the proton’s trajectory, including its shape and orientation.
**Key Parameters:**
- Initial speed of the proton: \(1.05 \times 10^6 \, \text{m/s}\)
- Magnetic field strength: \(0.295 \, \text{T}\)
- Direction of magnetic field: Vertical (upward)
**Tasks:**
1. Determine the radius of the path.
2. Describe the proton's trajectory.
**Input Fields:**
1. **The radius of the path:** [Insert Input Box]
2. **The proton’s trajectory:** [Dropdown Menu - Select from options]
### Solution Approach
**Step 1: Understanding the Trajectory**
- When a charged particle such as a proton moves in a uniform magnetic field perpendicular to its velocity, it experiences a centripetal force that makes it move in a circular path.
- The trajectory of the proton in this case will be a circle perpendicular to the magnetic field, with the plane of the circle oriented horizontally.
**Step 2: Calculating the Radius**
- The radius of the path \(r\) can be found using the formula \(r = \frac{mv}{qB}\), where:
- \(m\) is the mass of the proton (\(1.67 \times 10^{-27} \, \text{kg}\))
- \(v\) is the velocity of the proton (\(1.05 \times 10^6 \, \text{m/s}\))
- \(q\) is the charge of the proton (\(1.6 \times 10^{-19} \, \text{C}\))
- \(B\) is the magnetic field strength (\(0.295 \, \text{T}\))
Insert these values to calculate the radius.
**Step 3: Describing the Trajectory**
- The proton moves in a circular trajectory in a plane perpendicular to the direction of the magnetic field.
- The proton's motion will be clockwise or counterclockwise depending on the direction of the magnetic force applied.
The detailed explanation includes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2379bb0-49c5-44f7-ac7a-000baa150133%2Fe3124261-1e5a-4f5f-985e-8b497ed284e5%2Fzqcf94i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Proton Trajectories in Uniform Magnetic Fields
**Problem Statement:**
A proton is initially moving west at a speed of \(1.05 \times 10^6 \, \text{m/s}\) in a uniform magnetic field of magnitude \(0.295 \, \text{T}\) directed vertically upward. Describe in detail the proton’s trajectory, including its shape and orientation.
**Key Parameters:**
- Initial speed of the proton: \(1.05 \times 10^6 \, \text{m/s}\)
- Magnetic field strength: \(0.295 \, \text{T}\)
- Direction of magnetic field: Vertical (upward)
**Tasks:**
1. Determine the radius of the path.
2. Describe the proton's trajectory.
**Input Fields:**
1. **The radius of the path:** [Insert Input Box]
2. **The proton’s trajectory:** [Dropdown Menu - Select from options]
### Solution Approach
**Step 1: Understanding the Trajectory**
- When a charged particle such as a proton moves in a uniform magnetic field perpendicular to its velocity, it experiences a centripetal force that makes it move in a circular path.
- The trajectory of the proton in this case will be a circle perpendicular to the magnetic field, with the plane of the circle oriented horizontally.
**Step 2: Calculating the Radius**
- The radius of the path \(r\) can be found using the formula \(r = \frac{mv}{qB}\), where:
- \(m\) is the mass of the proton (\(1.67 \times 10^{-27} \, \text{kg}\))
- \(v\) is the velocity of the proton (\(1.05 \times 10^6 \, \text{m/s}\))
- \(q\) is the charge of the proton (\(1.6 \times 10^{-19} \, \text{C}\))
- \(B\) is the magnetic field strength (\(0.295 \, \text{T}\))
Insert these values to calculate the radius.
**Step 3: Describing the Trajectory**
- The proton moves in a circular trajectory in a plane perpendicular to the direction of the magnetic field.
- The proton's motion will be clockwise or counterclockwise depending on the direction of the magnetic force applied.
The detailed explanation includes
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