**Educational Text for Website:****Understanding Electron Motion in an Electric Field**In this example, we study how an electron, initially at rest, moves through a potential difference and how it interacts with an electric field between two parallel plates.**Scenario Description:**An electron is accelerated from rest through a potential difference \( V_1 = 1.13 \, \text{kV} \) before it enters the gap between two parallel plates. These plates have a separation of \( d = 24.3 \, \text{mm} \) and hold a potential difference of \( V_2 = 74.2 \, \text{V} \). The lower plate is at the lower potential. For simplicity, fringing effects are neglected. Here, we need to determine the magnetic field that will ensure the electron travels in a straight line between the plates.**Diagram Explanation:**The diagram shows the electron entering from the left through \( V_1 \), represented as a dashed horizontal line. The plates are parallel and separated by distance \( d \), with the electric field acting vertically between them. The electron enters horizontally, indicating that its velocity vector is perpendicular to the electric field vector.**Objective:**Using unit-vector notation, identify the correct magnetic field (expressed in milliteslas, mT) that allows the electron to travel in a straight line in the presence of the described electric field.Below the scenario, fields allow for the input of the magnetic field components along the \( \mathbf{i} \), \( \mathbf{j} \), and \( \mathbf{k} \) axes. The focus is particularly on determining the correct values needed to counteract the electric forces being exerted on the electron, ensuring a linear trajectory.

V1 = 1.13 kV = 1.13 x 103 V d = 24.3 mm = 0.0243 m V2 = 74.2 V

In the figure, an electron accelerated from rest through potential difference V1=1.13 kV enters the gap between two parallel plates having separation d = 24.3 mm and potential difference V2= 74.2 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number k) Units mT

In the figure, an electron accelerated from rest through potential difference V1=1.13 kV enters the gap between two parallel plates having separation d = 24.3 mm and potential difference V2= 74.2 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number k) Units mT

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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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

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**Educational Text for Website:**

**Understanding Electron Motion in an Electric Field**

In this example, we study how an electron, initially at rest, moves through a potential difference and how it interacts with an electric field between two parallel plates.

**Scenario Description:**

An electron is accelerated from rest through a potential difference \( V_1 = 1.13 \, \text{kV} \) before it enters the gap between two parallel plates. These plates have a separation of \( d = 24.3 \, \text{mm} \) and hold a potential difference of \( V_2 = 74.2 \, \text{V} \). The lower plate is at the lower potential. For simplicity, fringing effects are neglected. Here, we need to determine the magnetic field that will ensure the electron travels in a straight line between the plates.

**Diagram Explanation:**

The diagram shows the electron entering from the left through \( V_1 \), represented as a dashed horizontal line. The plates are parallel and separated by distance \( d \), with the electric field acting vertically between them. The electron enters horizontally, indicating that its velocity vector is perpendicular to the electric field vector.

**Objective:**

Using unit-vector notation, identify the correct magnetic field (expressed in milliteslas, mT) that allows the electron to travel in a straight line in the presence of the described electric field.

Below the scenario, fields allow for the input of the magnetic field components along the \( \mathbf{i} \), \( \mathbf{j} \), and \( \mathbf{k} \) axes. The focus is particularly on determining the correct values needed to counteract the electric forces being exerted on the electron, ensuring a linear trajectory.

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