(III) In a given CRT, electrons are accelerated horizontally by 7.2 kV . They then pass through

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(III) In a given CRT, electrons are accelerated horizontally...

(III) In a given CRT, electrons are accelerated horizontally by 7.2 $\mathrm{kV}$ . They then pass through a uniform electric field $E$ for a distance of 2.8 $\mathrm{cm}$ which deflects them upward so they reach the top of the screen 22 $\mathrm{cm}$ away, 11 $\mathrm{cm}$ above the center. Estimate the value of $E .$

Key Concepts

Kinematics of Charged Particles in an Electric Field

The motion of charged particles under the influence of an electric field can be described using kinematic equations. Since the electric field applies a constant force (hence constant acceleration) in a given direction, the deflection of the particle’s path can be calculated by treating the problem as a projectile motion scenario, where one component of the motion is influenced by the field while the other remains constant.

Application in Cathode Ray Tubes (CRTs)

Cathode ray tubes utilize accelerated electrons, which are steered by electric fields, to create visible images on a screen. Understanding the process of electron acceleration and subsequent deflection due to electric fields is essential for manipulating the electron paths to form the desired patterns on the screen.

Energy Conversion in Accelerated Charges

When a charged particle such as an electron accelerates through a potential difference, its electric potential energy is converted into kinetic energy. This conversion is governed by the relationship between the work done by the electric field and the gain in kinetic energy, which is foundational in understanding the dynamics of charged particles in devices like CRTs.

Force on a Charged Particle in an Electric Field

A charged particle in an electric field experiences a force proportional to both the charge and the electric field strength (F = qE). This force is responsible for deviations in the particle’s trajectory, and it plays a central role in analyzing and predicting the behavior of charged particles subjected to uniform or varying electric fields.

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