A proton is released from rest in a uniform electric field...

A proton is released from rest in a uniform electric field of magnitude $1.08 \times 10^{5} \mathrm{N} / \mathrm{C}$. Find the speed of the proton after it has traveled
(a) $1.00 \mathrm{cm}$ and
(b) $10.0 \mathrm{cm}$

Key Concepts

Work-Energy Principle

The work-energy principle states that the work done on a particle by a force is equal to the change in its kinetic energy. In the context of electric fields, the work done by the electric force over a displacement can be equated to the kinetic energy gained by the charged particle. This approach offers an alternative method to solve for the particle’s speed without directly using kinematic equations.

Kinematics for Constant Acceleration

Kinematic equations are used to relate the displacement, initial velocity, acceleration, and final velocity of an object undergoing constant acceleration. When the force (and thus the acceleration) on a charged particle in a uniform electric field is constant, these equations provide reliable methods to determine quantities such as the velocity after a certain displacement.

Uniform Electric Field

A uniform electric field is one in which the electric field vector has the same magnitude and direction at every point in space. This consistency simplifies the analysis of charged particles moving within the field because the force experienced by the particle remains constant, which is essential when applying equations of motion or energy conservation principles.

Force on a Charged Particle

The force experienced by a charged particle in an electric field is given by F = qE, where q is the charge and E is the electric field. This fundamental concept, derived from Coulomb’s law, dictates how the particle will accelerate in the field, making it a key consideration in problems involving motion in electric fields.

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