An electron is projected horizontally into the space between...

An electron is projected horizontally into the space between two oppositely charged metal plates. The electric field between the plates is $500.0 \mathrm{N} / \mathrm{C},$ directed up. (a) While in the field, what is the force on the electron? (b) If the vertical deflection of the electron as it leaves the plates is $3.00 \mathrm{mm},$ how much has its kinetic energy increased due to the electric field?

An electron is projected horizontally into the space between two oppositely charged metal plates. The electric field between the plates is $500.0 \mathrm{N} / \mathrm{C},$ directed up.
(a) While in the field, what is the force on the electron?
(b) If the vertical deflection of the electron as it leaves the plates is $3.00 \mathrm{mm},$ how much has its kinetic energy increased due to the electric field?

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Key Concepts

Energy Transformation in Electric Fields

When a charged particle, such as an electron, accelerates in an electric field, the field does work on the particle, converting potential energy into kinetic energy. This concept is essential in understanding how electric fields can increase the kinetic energy of charged particles.

Work-Energy Theorem in Electrical Context

The work done by the electric field on a charged particle as it moves a certain distance leads to a change in the particle's kinetic energy. This is encapsulated by the work-energy theorem, which states that the net work done on an object equals its change in kinetic energy.

Force on a Charged Particle

The force on a charged particle in an electric field is given by the product of the charge and the electric field (F = qE). This relationship not only explains the magnitude of the force but also its direction, which depends on the sign of the charge.

Electric Field

An electric field represents a region in space where a charged particle experiences a force. The magnitude and direction of this field determine the force on a charge placed within it, and in uniform fields, this force is constant in both magnitude and direction.

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