c) Each particle follows a circular path with constant radius while in the uniform B field. Show that the radiu of the circular path is given by the following relationship: ту R = qB field strength. where R is the radius, m is the mass, v is the velocity, q is the charge, and B is the magnetic d) All of the particles have the same speeds as they enter the B-Field. Determine the particle with the larges charge to mass ratio.
c) Each particle follows a circular path with constant radius while in the uniform B field. Show that the radiu of the circular path is given by the following relationship: ту R = qB field strength. where R is the radius, m is the mass, v is the velocity, q is the charge, and B is the magnetic d) All of the particles have the same speeds as they enter the B-Field. Determine the particle with the larges charge to mass ratio.
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Chapter1: Units, Trigonometry. And Vectors
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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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Displacement, Velocity and Acceleration
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Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
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Note: Velocity is constant.
![### Magnetic Fields and Motion of Charged Particles
When charged particles enter a region with a uniform magnetic field, they follow unique paths due to the Lorentz force acting on them. Understanding the motion of these particles can help us explore fundamental principles in electromagnetism.
#### Particle Motion in a Uniform Magnetic Field
1. **Charged Particles in B-Field:**
Four particles move from space with no external fields into a region with a uniform magnetic field (uniform B-field). Each particle enters and exits the uniform magnetic field as shown in the diagram below.
![Graphical Representation]
The diagram depicts four particles (Particle 1, Particle 2, Particle 3, and Particle 4), each following distinct paths as they move through the uniform magnetic field. The paths are as follows:
- Particle 1 (green): Moves straight upwards.
- Particle 2 (purple): Moves in a semi-circular path and exits to the right.
- Particle 3 (blue): Moves in a semi-circular path and exits to the left.
- Particle 4 (orange): Moves in a quarter-circular path and exits downwards.
2. **Radius of Circular Path:**
Each particle follows a circular path with a constant radius while in the uniform B-field. The radius \( R \) of the circular path is derived from the following relationship:
\[
R = \frac{mv}{qB}
\]
Where:
- \( R \): Radius of the circular path
- \( m \): Mass of the particle
- \( v \): Velocity of the particle
- \( q \): Charge of the particle
- \( B \): Magnetic field strength
3. **Charge to Mass Ratio:**
All the particles have the same speeds as they enter the magnetic field (B-field). In order to determine the particle with the largest charge to mass ratio \(\left( \frac{q}{m} \right)\), we analyze their paths. The particle with the smallest path radius has the largest charge to mass ratio, as \( R \) is inversely proportional to \(\frac{q}{m}\).
By carefully studying the paths shown in the diagram, we compare the radii. From visual inspection:
- Particle 4 shows the smallest radius.
- Therefore, Particle 4 has the largest charge to mass ratio.
This fundamental illustration demonstrates how](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdff7b543-7c53-4567-b2e2-82ba64a4a215%2F239cc5d2-1ad5-427c-a2fe-81f77833894f%2Fkmd1qsd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Magnetic Fields and Motion of Charged Particles
When charged particles enter a region with a uniform magnetic field, they follow unique paths due to the Lorentz force acting on them. Understanding the motion of these particles can help us explore fundamental principles in electromagnetism.
#### Particle Motion in a Uniform Magnetic Field
1. **Charged Particles in B-Field:**
Four particles move from space with no external fields into a region with a uniform magnetic field (uniform B-field). Each particle enters and exits the uniform magnetic field as shown in the diagram below.
![Graphical Representation]
The diagram depicts four particles (Particle 1, Particle 2, Particle 3, and Particle 4), each following distinct paths as they move through the uniform magnetic field. The paths are as follows:
- Particle 1 (green): Moves straight upwards.
- Particle 2 (purple): Moves in a semi-circular path and exits to the right.
- Particle 3 (blue): Moves in a semi-circular path and exits to the left.
- Particle 4 (orange): Moves in a quarter-circular path and exits downwards.
2. **Radius of Circular Path:**
Each particle follows a circular path with a constant radius while in the uniform B-field. The radius \( R \) of the circular path is derived from the following relationship:
\[
R = \frac{mv}{qB}
\]
Where:
- \( R \): Radius of the circular path
- \( m \): Mass of the particle
- \( v \): Velocity of the particle
- \( q \): Charge of the particle
- \( B \): Magnetic field strength
3. **Charge to Mass Ratio:**
All the particles have the same speeds as they enter the magnetic field (B-field). In order to determine the particle with the largest charge to mass ratio \(\left( \frac{q}{m} \right)\), we analyze their paths. The particle with the smallest path radius has the largest charge to mass ratio, as \( R \) is inversely proportional to \(\frac{q}{m}\).
By carefully studying the paths shown in the diagram, we compare the radii. From visual inspection:
- Particle 4 shows the smallest radius.
- Therefore, Particle 4 has the largest charge to mass ratio.
This fundamental illustration demonstrates how
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