Understanding the Forces
* Electric Force: A charged particle in an electric field experiences a force due to the field. This force is given by:
* F = qE
* F is the electric force (in Newtons)
* q is the charge of the particle (in Coulombs)
* E is the electric field strength (in Newtons per Coulomb or Volts per meter)
* Newton's Second Law: This fundamental law relates force, mass, and acceleration:
* F = ma
* F is the net force acting on an object (in Newtons)
* m is the mass of the object (in kilograms)
* a is the acceleration of the object (in meters per second squared)
Deriving the Acceleration
1. Equating Forces: Since the electric force is the only force acting on the charged particle, we can equate the two expressions for force:
* qE = ma
2. Solving for Acceleration: Divide both sides of the equation by the mass (m) to isolate the acceleration:
* a = (qE) / m
Key Points:
* Direction: The direction of the acceleration is the same as the direction of the electric field if the charge is positive, and opposite the direction of the field if the charge is negative.
* Uniform Field: This derivation assumes a uniform electric field. If the field is non-uniform, the acceleration will vary depending on the field strength at the particle's location.
Example:
Imagine an electron (charge -1.602 x 10^-19 C, mass 9.109 x 10^-31 kg) moving in a uniform electric field of strength 100 N/C.
* The acceleration of the electron would be:
* a = (-1.602 x 10^-19 C * 100 N/C) / (9.109 x 10^-31 kg)
* a ≈ -1.76 x 10^13 m/s²
The negative sign indicates that the electron accelerates in the direction opposite to the electric field (since it's negatively charged).
