A particle with an unknown mass and charge moves with a constant speed of v = 2.2 x 106 m/s as it passes un-deflected through a pair of parallel plates as shown. The plates are separated by a distance of d = 5.0 x 10-3m, and a constant potential difference V is maintained between them. A uniform magnetic field of B = 1.20 T directed into the page exists between the plates and to the right of them as shown. After the particle passes into the region to the right of the plates where only the magnetic field exists, its trajectory is circular with radius r = 0.10 m. Determine the charge sign and charge/mass ratio of the particle, and the electric field direction and potential difference magnitude for plates. ### Description of the Diagram:This schematic diagram illustrates the deflection of a charged particle in a magnetic field.#### Key Components:1. **Ammeter (A):** - Positioned in the circuit, it measures the electric current flowing through it.2. **Parallel Plates:** - Two horizontal parallel plates are displayed. The space between them forms a part of the pathway for charged particles.3. **Magnetic Field:** - Represented by the pattern of "X"s, indicating that the magnetic field points into the page (perpendicular to the plane of the diagram).4. **Velocity (V):** - The straight arrow labeled "V" indicates the initial velocity vector of a charged particle moving between the plates.5. **Curved Path with Radius (R):** - The particle, after entering the magnetic field, follows a curved path. The radius of curvature of this path is labeled "R".### Explanation:- **Charged Particle Motion:** - A charged particle enters the region between the parallel plates with an initial velocity "V". The constant magnetic field perpendicular to the velocity vector exerts a force on the particle, deflecting it along a curved path. - **Magnetic Force:** - The direction of the magnetic force is determined by the right-hand rule. The force is always perpendicular to the velocity of the particle, leading to circular motion.- **Radius of Curvature (R):** - The radius of the particle's path "R" is determined by the balance between magnetic force and the centripetal force needed for circular motion. This diagram is used to demonstrate fundamental principles of electromagnetism, including the effect of magnetic fields on moving charges, which is fundamental in applications like mass spectrometry and cyclotrons.

The information given is as follows: 1. The speed of the particle, v=2.2×106 m/s 2. The separation…

Answered: A particle with an unknown mass and…

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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A particle with an unknown mass and charge moves with a constant speed
of v = 2.2 x 10⁶ m/s as it passes un-deflected through a pair of parallel
plates as shown. The plates are separated by a distance of d = 5.0 x 10^-3
m, and a constant potential difference V is maintained between them. A
uniform magnetic field of B = 1.20 T directed into the page exists between
the plates and to the right of them as shown. After the particle passes
into the region to the right of the plates where only the magnetic field
exists, its trajectory is circular with radius r = 0.10 m. Determine the charge sign and charge/mass ratio of the particle, and the electric field direction and potential difference magnitude for plates.

### Description of the Diagram:

This schematic diagram illustrates the deflection of a charged particle in a magnetic field.

#### Key Components:

1. **Ammeter (A):**
- Positioned in the circuit, it measures the electric current flowing through it.

2. **Parallel Plates:**
- Two horizontal parallel plates are displayed. The space between them forms a part of the pathway for charged particles.

3. **Magnetic Field:**
- Represented by the pattern of "X"s, indicating that the magnetic field points into the page (perpendicular to the plane of the diagram).

4. **Velocity (V):**
- The straight arrow labeled "V" indicates the initial velocity vector of a charged particle moving between the plates.

5. **Curved Path with Radius (R):**
- The particle, after entering the magnetic field, follows a curved path. The radius of curvature of this path is labeled "R".

### Explanation:

- **Charged Particle Motion:**
- A charged particle enters the region between the parallel plates with an initial velocity "V". The constant magnetic field perpendicular to the velocity vector exerts a force on the particle, deflecting it along a curved path.

- **Magnetic Force:**
- The direction of the magnetic force is determined by the right-hand rule. The force is always perpendicular to the velocity of the particle, leading to circular motion.

- **Radius of Curvature (R):**
- The radius of the particle's path "R" is determined by the balance between magnetic force and the centripetal force needed for circular motion.

This diagram is used to demonstrate fundamental principles of electromagnetism, including the effect of magnetic fields on moving charges, which is fundamental in applications like mass spectrometry and cyclotrons.

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