A proton, a deuteron (q = +e, m = 2.0 u), and an alpha particle (q = 2e, m = 4.0 u) are accelerated through the same potential difference and then enter the same region of uniform magnetic field B,moving perpendicular to B .(a) What is the ratio of the proton's kinetic energy Kp to the alpha particle's kinetic energy Kg? (b) What is the ratio of deuteron's kinetic energy Ka to Ka? Assume that the radius of the proton's circular path is 11.5 cm. (c) What is the radius of the deuteron's path? (d) What is the radius of the alpha particle's path? (a) Number i Units (b) Number i Units (c) Number i Units
A proton, a deuteron (q = +e, m = 2.0 u), and an alpha particle (q = 2e, m = 4.0 u) are accelerated through the same potential difference and then enter the same region of uniform magnetic field B,moving perpendicular to B .(a) What is the ratio of the proton's kinetic energy Kp to the alpha particle's kinetic energy Kg? (b) What is the ratio of deuteron's kinetic energy Ka to Ka? Assume that the radius of the proton's circular path is 11.5 cm. (c) What is the radius of the deuteron's path? (d) What is the radius of the alpha particle's path? (a) Number i Units (b) Number i Units (c) Number i Units
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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![**Physics Problem: Motion of Charged Particles in a Magnetic Field**
**Problem Statement:**
A proton, a deuteron (\( q = +e, m = 2.0 \, u \)), and an alpha particle (\( q = 2e, m = 4.0 \, u \)) are accelerated through the same potential difference and then enter the same region of uniform magnetic field \( \mathbf{B} \), moving perpendicular to \( \mathbf{B} \).
1. **Question (a):** What is the ratio of the proton's kinetic energy \( K_p \) to the alpha particle's kinetic energy \( K_a \)?
- **Answer (a):**
[ ] Number [ ] Units
2. **Question (b):** What is the ratio of deuteron's kinetic energy \( K_d \) to \( K_a \)?
- **Answer (b):**
[ ] Number [ ] Units
3. **Question (c):** Assume that the radius of the proton's circular path is 11.5 cm. What is the radius of the deuteron's path?
- **Answer (c):**
[ ] Number [ ] Units
4. **Question (d):** What is the radius of the alpha particle's path?
- **Answer (d):**
[ ] Number [ ] Units
**Instructions for Students:**
- Enter your answers in the provided fields.
- Ensure that you provide units where indicated.
- Review the relevance of the formula \( r = \frac{mv}{qB} \) and how energy conservation principles apply to particles accelerated by the same potential difference.
This problem aims to test your understanding of the motion of charged particles in magnetic fields, kinetic energy relationships, and circular motion. Ensure to review related principles and solve comprehensively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8b65224-21df-49da-a8da-84f6a1af571d%2Fbe269317-aaa6-434a-8b0d-3250e141b9f7%2F0t7rsjn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Motion of Charged Particles in a Magnetic Field**
**Problem Statement:**
A proton, a deuteron (\( q = +e, m = 2.0 \, u \)), and an alpha particle (\( q = 2e, m = 4.0 \, u \)) are accelerated through the same potential difference and then enter the same region of uniform magnetic field \( \mathbf{B} \), moving perpendicular to \( \mathbf{B} \).
1. **Question (a):** What is the ratio of the proton's kinetic energy \( K_p \) to the alpha particle's kinetic energy \( K_a \)?
- **Answer (a):**
[ ] Number [ ] Units
2. **Question (b):** What is the ratio of deuteron's kinetic energy \( K_d \) to \( K_a \)?
- **Answer (b):**
[ ] Number [ ] Units
3. **Question (c):** Assume that the radius of the proton's circular path is 11.5 cm. What is the radius of the deuteron's path?
- **Answer (c):**
[ ] Number [ ] Units
4. **Question (d):** What is the radius of the alpha particle's path?
- **Answer (d):**
[ ] Number [ ] Units
**Instructions for Students:**
- Enter your answers in the provided fields.
- Ensure that you provide units where indicated.
- Review the relevance of the formula \( r = \frac{mv}{qB} \) and how energy conservation principles apply to particles accelerated by the same potential difference.
This problem aims to test your understanding of the motion of charged particles in magnetic fields, kinetic energy relationships, and circular motion. Ensure to review related principles and solve comprehensively.
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