A proton travelling at 9.74E3 m/s suddenly enters in a uniform magnetic field of 6.05 T. The proton travels at an angle of θ = 35.3º with the field lines, as shown in the figure. What is the magnetic force on the proton (use positive sign if the force points out of page and negative sign if the force points into page) (in N)?
A proton travelling at 9.74E3 m/s suddenly enters in a uniform magnetic field of 6.05 T. The proton travels at an angle of θ = 35.3º with the field lines, as shown in the figure. What is the magnetic force on the proton (use positive sign if the force points out of page and negative sign if the force points into page) (in N)?
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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A proton travelling at 9.74E3 m/s suddenly enters in a uniform magnetic field of 6.05 T. The proton travels at an angle of θ = 35.3º with the field lines, as shown in the figure. What is the magnetic force on the proton (use positive sign if the force points out of page and negative sign if the force points into page) (in N)?
![### Understanding the Relationship Between Velocity and Magnetic Field
#### Diagram Explanation
This diagram illustrates the relationship between a velocity vector (\(\vec{v}\)) and a magnetic field vector (\(\vec{B}\)).
- **Velocity Vector (\(\vec{v}\)):** Represented by a red arrow pointing upwards. This indicates the direction in which an object is moving.
- **Magnetic Field Vector (\(\vec{B}\)):** Represented by a blue arrow angled to the right. This indicates the direction of the magnetic field in which the object is moving.
- **Angle (\(\theta\)):** The angle between the velocity vector \(\vec{v}\) and the magnetic field vector \(\vec{B}\). This angle is crucial in determining the force experienced by the moving charge in the magnetic field.
#### Key Concepts
1. **Lorentz Force:**
- When a charged particle moves through a magnetic field, it experiences a force perpendicular to both the velocity of the particle and the direction of the magnetic field. This force is known as the Lorentz force.
- The magnitude of the force can be calculated using the equation:
\[ F = q(\vec{v} \times \vec{B}) = qvB \sin(\theta) \]
where \(q\) is the charge of the particle, \(v\) is the speed of the particle, \(B\) is the magnitude of the magnetic field, and \(\theta\) is the angle between \(\vec{v}\) and \(\vec{B}\).
2. **Right-Hand Rule:**
- To determine the direction of the force acting on a positive charge, use the right-hand rule: Point your thumb in the direction of \(\vec{v}\) (velocity), your fingers in the direction of \(\vec{B}\) (magnetic field), and your palm will face in the direction of the resultant force (\(\vec{F}\)).
This diagram is a fundamental illustration in the study of electromagnetism, providing a visual representation of how magnetic fields interact with moving charges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb234898a-ca00-4740-ae3d-79576f672843%2F9cd4dedf-602a-44c6-853a-fe3ed920b1ca%2Fv91bxod_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Relationship Between Velocity and Magnetic Field
#### Diagram Explanation
This diagram illustrates the relationship between a velocity vector (\(\vec{v}\)) and a magnetic field vector (\(\vec{B}\)).
- **Velocity Vector (\(\vec{v}\)):** Represented by a red arrow pointing upwards. This indicates the direction in which an object is moving.
- **Magnetic Field Vector (\(\vec{B}\)):** Represented by a blue arrow angled to the right. This indicates the direction of the magnetic field in which the object is moving.
- **Angle (\(\theta\)):** The angle between the velocity vector \(\vec{v}\) and the magnetic field vector \(\vec{B}\). This angle is crucial in determining the force experienced by the moving charge in the magnetic field.
#### Key Concepts
1. **Lorentz Force:**
- When a charged particle moves through a magnetic field, it experiences a force perpendicular to both the velocity of the particle and the direction of the magnetic field. This force is known as the Lorentz force.
- The magnitude of the force can be calculated using the equation:
\[ F = q(\vec{v} \times \vec{B}) = qvB \sin(\theta) \]
where \(q\) is the charge of the particle, \(v\) is the speed of the particle, \(B\) is the magnitude of the magnetic field, and \(\theta\) is the angle between \(\vec{v}\) and \(\vec{B}\).
2. **Right-Hand Rule:**
- To determine the direction of the force acting on a positive charge, use the right-hand rule: Point your thumb in the direction of \(\vec{v}\) (velocity), your fingers in the direction of \(\vec{B}\) (magnetic field), and your palm will face in the direction of the resultant force (\(\vec{F}\)).
This diagram is a fundamental illustration in the study of electromagnetism, providing a visual representation of how magnetic fields interact with moving charges.
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