### Electrons in Magnetic Fields: An Educational ExerciseElectrons starting from rest are accelerated through a potential difference of \( 210 \, \text{V} \) and fired into a region of uniform \( 2.8 \, \text{mT} \) magnetic field generated by a large solenoid. The electrons are initially moving in the \( +x \)-direction upon entering the field, and the field is directed out of the page. (Assume that the \( +x \)-axis is to the right, the \( +y \)-axis is up along the page, and the \( +z \)-axis is out of the page.)1. **Determine the radius (in m) of the circle in which the electrons will move in this uniform magnetic field.** \[ \boxed{\phantom{m}} \]2. **Determine the initial direction of the magnetic force the electrons feel upon entering the uniform field of the solenoid.** - [ ] \( +x \)-direction - [ ] \( -x \)-direction - [ ] \( +y \)-direction - [ ] \( -y \)-direction**Explanation of Concepts:**- **Potential Difference (Voltage):** A measure of the electric potential energy per unit charge. Here, it accelerates the electrons to a certain velocity. - **Magnetic Field (B-field):** A field produced by electric currents and magnetic dipoles, influencing the motion of charged particles like electrons. In this scenario, the magnetic field is uniform and directed out of the page.- **Electron Motion in Magnetic Field:** When charged particles move in a magnetic field, they experience a force perpendicular to both their velocity and the magnetic field (Lorentz force). This force is responsible for the circular motion of the electrons.### Detailed Analysis:- **Part (a) Calculation:** To determine the radius of the circular path, we use the relationship between the centripetal force due to magnetic field and the kinetic energy gained by the electrons from the potential difference.- **Part (b) Direction of Magnetic Force:** Using the right-hand rule for negative charges (electrons), we can determine the direction of the initial magnetic force exerted on the electrons upon entering the magnetic field.### Note:If students need further assistance, they should review concepts such as the Lorentz force, the relationship between kinetic energy and velocity, and the right-hand

Electrons starting from rest are accelerated through a potential difference of 210 V and fired into a region of uniform 2.8 mT magnetic field generated by a large solenoid. The electrons are initially moving in the +x-direction upon entering the field, and the field is directed out of the page. (Assume that the +x-axis is to the right, the +y-axis is up along the page, and the +z- axis is out of the page.) (a) Determine the radius (in m) of the circle in which the electrons will move in this uniform magnetic field. (b) Determine the initial direction of the magnetic force the electrons feel upon entering the uniform fleld of the solenoid. O +x-direction O -x-direction O +y-directlon O-y-direction

Electrons starting from rest are accelerated through a potential difference of 210 V and fired into a region of uniform 2.8 mT magnetic field generated by a large solenoid. The electrons are initially moving in the +x-direction upon entering the field, and the field is directed out of the page. (Assume that the +x-axis is to the right, the +y-axis is up along the page, and the +z- axis is out of the page.) (a) Determine the radius (in m) of the circle in which the electrons will move in this uniform magnetic field. (b) Determine the initial direction of the magnetic force the electrons feel upon entering the uniform fleld of the solenoid. O +x-direction O -x-direction O +y-directlon O-y-direction

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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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

### Electrons in Magnetic Fields: An Educational Exercise

Electrons starting from rest are accelerated through a potential difference of \( 210 \, \text{V} \) and fired into a region of uniform \( 2.8 \, \text{mT} \) magnetic field generated by a large solenoid. The electrons are initially moving in the \( +x \)-direction upon entering the field, and the field is directed out of the page. (Assume that the \( +x \)-axis is to the right, the \( +y \)-axis is up along the page, and the \( +z \)-axis is out of the page.)

1. **Determine the radius (in m) of the circle in which the electrons will move in this uniform magnetic field.**

\[ \boxed{\phantom{m}} \]

2. **Determine the initial direction of the magnetic force the electrons feel upon entering the uniform field of the solenoid.**

- [ ] \( +x \)-direction
- [ ] \( -x \)-direction
- [ ] \( +y \)-direction
- [ ] \( -y \)-direction

**Explanation of Concepts:**

- **Potential Difference (Voltage):** A measure of the electric potential energy per unit charge. Here, it accelerates the electrons to a certain velocity.

- **Magnetic Field (B-field):** A field produced by electric currents and magnetic dipoles, influencing the motion of charged particles like electrons. In this scenario, the magnetic field is uniform and directed out of the page.

- **Electron Motion in Magnetic Field:** When charged particles move in a magnetic field, they experience a force perpendicular to both their velocity and the magnetic field (Lorentz force). This force is responsible for the circular motion of the electrons.

### Detailed Analysis:

- **Part (a) Calculation:** To determine the radius of the circular path, we use the relationship between the centripetal force due to magnetic field and the kinetic energy gained by the electrons from the potential difference.

- **Part (b) Direction of Magnetic Force:** Using the right-hand rule for negative charges (electrons), we can determine the direction of the initial magnetic force exerted on the electrons upon entering the magnetic field.

### Note:
If students need further assistance, they should review concepts such as the Lorentz force, the relationship between kinetic energy and velocity, and the right-hand

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