Protons having a kinetic energy of 3.10 MeV are moving in the positive x-direction and enter a magnetic field of 0.0670 T in the z-direction, out of the plane of the page, and extending from x = 0 to x = 1.00 m as in the figure below. A diagram contains a proton and field lines plotted on an x y coordinate plane, where the +x-axis is to the right and the +y-axis is upward. The proton enters the diagram from the left along the −x-axis, with an arrow extending from the proton pointing toward the right. Magnetic field lines point out of the page for all points on the x y plane for which 0 ≤ x ≤ 1.00 m. A dashed curve extends from the proton directly to the right along the −x-axis to the origin, enters the region of field and curves down and to the right, then leaves the field and points down and to the right in a straight line. (a) Calculate the y-component of the protons' momentum as they leave the magnetic field. (Indicate the direction with the sign of your answer.) kg · m/s (b) Find the angle ? between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. Hint: Neglect relativistic effects and note that 1 eV = 1.60 10-19 J.
Protons having a kinetic energy of 3.10 MeV are moving in the positive x-direction and enter a magnetic field of 0.0670 T in the z-direction, out of the plane of the page, and extending from x = 0 to x = 1.00 m as in the figure below. A diagram contains a proton and field lines plotted on an x y coordinate plane, where the +x-axis is to the right and the +y-axis is upward. The proton enters the diagram from the left along the −x-axis, with an arrow extending from the proton pointing toward the right. Magnetic field lines point out of the page for all points on the x y plane for which 0 ≤ x ≤ 1.00 m. A dashed curve extends from the proton directly to the right along the −x-axis to the origin, enters the region of field and curves down and to the right, then leaves the field and points down and to the right in a straight line. (a) Calculate the y-component of the protons' momentum as they leave the magnetic field. (Indicate the direction with the sign of your answer.) kg · m/s (b) Find the angle ? between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. Hint: Neglect relativistic effects and note that 1 eV = 1.60 10-19 J.
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Protons having a kinetic energy of 3.10 MeV are moving in the positive x-direction and enter a magnetic field of 0.0670 T in the z-direction, out of the plane of the page, and extending from x = 0 to x = 1.00 m as in the figure below.
A diagram contains a proton and field lines plotted on an x y coordinate plane, where the +x-axis is to the right and the +y-axis is upward. The proton enters the diagram from the left along the −x-axis, with an arrow extending from the proton pointing toward the right. Magnetic field lines point out of the page for all points on the x y plane for which 0 ≤ x ≤ 1.00 m. A dashed curve extends from the proton directly to the right along the −x-axis to the origin, enters the region of field and curves down and to the right, then leaves the field and points down and to the right in a straight line.
(a) Calculate the y-component of the protons' momentum as they leave the magnetic field. (Indicate the direction with the sign of your answer.)
kg · m/s
(b) Find the angle ? between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. Hint: Neglect relativistic effects and note that 1 eV = 1.60 10-19 J.
? = °
kg · m/s
(b) Find the angle ? between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. Hint: Neglect relativistic effects and note that 1 eV = 1.60 10-19 J.
? = °
![**Protons in a Magnetic Field**
Protons having a kinetic energy of **3.10 MeV** are moving in the positive x-direction and enter a magnetic field of **0.0670 T** in the z-direction, out of the plane of the page, and extending from \( x = 0 \) to \( x = 1.00 \, \text{m} \) as in the figure below.
**Diagram Explanation:**
- The diagram shows a proton (denoted by \( p \)) moving along the x-axis in the positive direction.
- A section of the path is covered with light green dots, indicating the magnetic field (\( B \)) oriented in the z-direction, perpendicular to the x-y plane.
- The field extends between \( x = 0 \) and \( x = 1.00 \, \text{m} \).
- The proton’s path is deflected downwards (in the negative y-direction) as it exits the magnetic field.
**Questions:**
(a) Calculate the y-component of the protons' momentum as they leave the magnetic field. (Indicate the direction with the sign of your answer.)
\[ \boxed{\ \ \ \ \ \ \ \ \ \ } \ \text{kg} \cdot \text{m/s} \]
(b) Find the angle \( \alpha \) between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. *Hint: Neglect relativistic effects and note that 1 eV = 1.60 × 10⁻¹⁹ J.*
\[ \alpha = \boxed{\ \ \ \ \ \ \ \ \ \ } \degree \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29d43c93-cd0d-4931-a587-6a4cf1783074%2F287b1065-e65c-4ab1-a4e1-435f73352059%2F0qqn0g6_processed.png&w=3840&q=75)
Transcribed Image Text:**Protons in a Magnetic Field**
Protons having a kinetic energy of **3.10 MeV** are moving in the positive x-direction and enter a magnetic field of **0.0670 T** in the z-direction, out of the plane of the page, and extending from \( x = 0 \) to \( x = 1.00 \, \text{m} \) as in the figure below.
**Diagram Explanation:**
- The diagram shows a proton (denoted by \( p \)) moving along the x-axis in the positive direction.
- A section of the path is covered with light green dots, indicating the magnetic field (\( B \)) oriented in the z-direction, perpendicular to the x-y plane.
- The field extends between \( x = 0 \) and \( x = 1.00 \, \text{m} \).
- The proton’s path is deflected downwards (in the negative y-direction) as it exits the magnetic field.
**Questions:**
(a) Calculate the y-component of the protons' momentum as they leave the magnetic field. (Indicate the direction with the sign of your answer.)
\[ \boxed{\ \ \ \ \ \ \ \ \ \ } \ \text{kg} \cdot \text{m/s} \]
(b) Find the angle \( \alpha \) between the initial velocity vector of the proton beam and the velocity vector after the beam emerges from the field. *Hint: Neglect relativistic effects and note that 1 eV = 1.60 × 10⁻¹⁹ J.*
\[ \alpha = \boxed{\ \ \ \ \ \ \ \ \ \ } \degree \]
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