Equation of Motion in a Uniform Electric Field
This page derives the equations of motion for a charged particle in a uniform electric field. The approach is similar to that used for the gravitational field, but with the electric force replacing gravity.
Definition: A uniform electric field is one where the electric field strength E is constant in magnitude and direction throughout the region of interest.
The derivation begins with Newton's second law in a Galilean reference frame, F = ma. For a particle with charge q in an electric field E, the force is given by Fe = qE.
Vocabulary: Electric field - A region in space where an electric charge experiences a force.
Equating the electric force to mass times acceleration yields:
a = qE/m
This acceleration is constant, similar to the gravitational case, but its magnitude depends on the charge-to-mass ratio of the particle.
The page then presents the initial conditions and integrates the acceleration equation twice to obtain the position equations:
x = V₀t
y = ½ × (qE/m) × t²
Example: These equations describe the motion of a charged particle initially moving horizontally in a vertical electric field.
The trajectory equation is derived by eliminating t:
y = (qE / (2mV₀²)) × x²
Highlight: This parabolic equation is crucial for solving Particule chargée dans un champ électrique uniforme exercices corrigés pdf problems.
The page concludes with a summary of the equations of motion and trajectory for a charged particle in a uniform electric field, providing a comprehensive set of tools for analyzing such systems.
